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In the present paper, we have obtained common best proximity point theorems of nonself maps in Hausdorff topological space. Further, our results extend the results due to Gerald F. Jungck, thereby proving a generalized version of Kirk's theorem (J. London Math. 1(1):107–111, 1969). [ABSTRACT FROM AUTHOR]

In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder's inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when T = N and T = R ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011). [ABSTRACT FROM AUTHOR]

In this paper, we obtain the Harary index and the hyper-Wiener index of the H-generalized join of graphs and the generalized corona product of graphs. As a consequence, we deduce some of the results in (Das et al. in J. Inequal. Appl. 2013:339, 2013) and (Khalifeh et al. in Comput. Math. Appl. 56:1402–1407, 2008). Moreover, we calculate the Harary index and the hyper-Wiener index of the ideal-based zero-divisor graph of a ring. [ABSTRACT FROM AUTHOR]

Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. [ABSTRACT FROM AUTHOR]

In this short paper we tackle two subjects. First, we provide a lower bound for the first eigenvalue of the antiperiodic problem for a Hill's equation based on L p -conditions, and as a consequence, we introduce an adjusted statement of the main result about the asymptotic stability of periodic solutions for the general Duffing equation in (Torres in Mediterr. J. Math. 1(4):479–486, 2004) (Theorem 4). This appropriate version of the result arises because of one subtlety in the proof provided in (Torres in Mediterr. J. Math. 1(4):479–486, 2004). More precisely, the lower bound of the first antiperiodic eigenvalue associated with Hill's equations of potential a (t) employed there may be negative, thus the conclusion is not completely attained. Hence, the adjustments considered here provide a mathematically correct result. On the other hand, we apply this result to obtain a lateral asymptotic stable periodic oscillation in the Comb-drive finger MEMS model with a cubic nonlinear stiffness term and linear damping. This fact is not typical in Comb-drive finger devices, thus our results could provide a new possibility; a new design principle for stabilization in Comb-drive finger MEMS. [ABSTRACT FROM AUTHOR]

The normalization of the combination of generalized Lommel–Wright function J κ 1 , κ 2 κ 3 , m (z) (m ∈ N , κ 3 > 0 and κ 1 , κ 2 ∈ C ) defined by J κ 1 , κ 2 κ 3 , m (z) : = Γ m (κ 1 + 1) Γ (κ 1 + κ 2 + 1) 2 2 κ 1 + κ 2 z 1 − (κ 2 / 2) − κ 1 J κ 1 , κ 2 κ 3 , m (z) , where J κ 1 , κ 2 κ 3 , m (z) : = (1 − 2 κ 1 − κ 2) J κ 1 , κ 2 κ 3 , m (z) + z (J κ 1 , κ 2 κ 3 , m (z)) ′ and J κ 1 , κ 2 κ 3 , m (z) = (z 2) 2 κ 1 + κ 2 ∑ n = 0 ∞ (− 1) n Γ m (n + κ 1 + 1) Γ (n κ 3 + κ 1 + κ 2 + 1) (z 2) 2 n , was previously introduced and some of its geometric properties have been considered. In this paper, we report conditions for J κ 1 , κ 2 κ 3 , m (z) to be starlike and convex of order α, 0 ≤ α < 1 , inside the open unit disk using some technical manipulations of the gamma and digamma functions, as well as inequality for the digamma function that has been proved (Guo and Qi in Proc. Am. Math. Soc. 141(3):1007–1015, 2013). In addition, a method presented by Lorch (J. Approx. Theory 40(2):115–120 1984) and further developed by Laforgia (Math. Compet. 42(166):597–600 1984) is applied to establish firstly sharp inequalities for the shifted factorial that will be used to obtain the order of starlikeness and convexity. We compare then the obtained orders of starlikeness and convexity with some important consequences in the literature as well as the results proposed by all techniques to demonstrate the accuracy of our approach. Ultimately, a lemma by (Fejér in Acta Litt. Sci. 8:89–115 1936) is used to prove that the modified form of the function J κ 1 , κ 2 κ 3 , m (z) defined by I κ 1 , κ 2 κ 3 , m (z) = J κ 1 , κ 2 κ 3 , m (z) ∗ z / (1 + z) is in the class of starlike and convex functions, respectively. Further work regarding the function J κ 1 , κ 2 κ 3 , m (z) is underway and will be presented in a forthcoming paper. [ABSTRACT FROM AUTHOR]

This paper deals with the blow-up phenomena connected to the following porous-medium problem with gradient terms under Robin boundary conditions: { u t = Δ u m + k 1 u p − k 2 | ∇ u | q in Ω × (0 , t ∗) , ∂ u ∂ ν + γ u = 0 on ∂ Ω × (0 , t ∗) , u (x , 0) = u 0 (x) ≥ 0 in Ω ‾ , where Ω ⊂ R n (n ≥ 3 ) is a bounded and convex domain with smooth boundary ∂Ω. The constants p, q, m are positive, and p > q > m > 1 , q > 2 . By making use of the Sobolev inequality and the differential inequality technique, we obtain a lower bound for the blow-up time of the solution. In addition, an example is given as an application of the abstract results obtained in this paper. Our results can be regarded as an answer to the open question raised by Li et al. in (Z. Angew. Math. Phys. 70:1–18, 2019). [ABSTRACT FROM AUTHOR]

We prove two key inequalities for metric and generalized projections in a certain Banach space. We then obtain some asymptotic behavior of a sequence generated by the shrinking projection method introduced by Takahashi et al. (J. Math. Anal. Appl. 341:276–286, 2008) where the computation allows some nonsummable errors. We follow the idea proposed by Kimura (Banach and Function Spaces IV (ISBFS 2012), pp. 303–311, 2014). The mappings studied in this paper are more general than the ones in (Ibaraki and Kimura in Linear Nonlinear Anal. 2:301–310, 2016; Ibaraki and Kajiba in Josai Math. Monogr. 11:105–120, 2018). In particular, the results in (Ibaraki and Kimura in Linear Nonlinear Anal. 2:301–310, 2016; Ibaraki and Kajiba in Josai Math. Monogr. 11:105–120, 2018) are both extended and supplemented. Finally, we discuss our results for finding a zero of maximal monotone operator and a minimizer of convex functions on a Banach space. [ABSTRACT FROM AUTHOR]

In this paper, some results on the complete moment convergence of extended negatively dependent (END) random variables are established. The results in the paper improve and extend the corresponding ones of Qiu et al. (Acta Math. Appl. Sin. 40(3):436–448, 2017) under some weaker conditions. Our results also improve and extend the related known works in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the monotonicity is investigated with respect to Orlicz sequence space l Φ , p equipped with the p-Amemiya norm, and the necessary and sufficient condition is obtained to guarantee the uniform monotonicity, locally uniform monotonicity, and strict monotonicity for l Φ , p . This completes the results of the paper (Cui et al. in J. Math. Anal. Appl. 432:1095–1105, 2015) which were obtained for the non-atomic measure space. Local upper and lower coefficients of monotonicity at any point of the unit sphere are calculated, l Φ , p is calculated. [ABSTRACT FROM AUTHOR]

The concept of Tribonacci sequence spaces by the domain of a regular Tribonacci matrix was introduced by Yaying and Hazarika (Math. Slovaca 70(3):697–706, 2000). In this paper, by using the domain of regular Tribonacci matrix T = (t i k) and the concept of neutrosophic convergence, we introduce some neutrosophic normed space in Tribonacci convergent spaces and prove some topological and algebraic properties based results with respect to these spaces. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce sharp upper and lower bounds to the ratio of two q-gamma functions Γ q (x + 1) / Γ q (x + s) for all real number s and 0 < q ≠ 1 in terms of the q-digamma function. Our results refine the results of Ismail and Muldoon (Internat. Ser. Numer. Math., vol. 119, pp. 309–323, 1994) and give the answer to the open problem posed by Alzer (Math. Nachr. 222(1):5–14, 2001). Also, for the classical gamma function, our results give a Kershaw inequality for all 0 < s < 1 when letting q → 1 and a new inequality for all s > 1 . [ABSTRACT FROM AUTHOR]

In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove a stochastic Fubini theorem by solving a special backward stochastic differential equation (BSDE, for short) which is different from the existing techniques. As an application, we obtain the well-posedness of a class of BSDEs with the Itô integral in drift term under a subtle Lipschitz condition. [ABSTRACT FROM AUTHOR]

In this paper, we present some new refinements of the Erdös-Mordell inequality, Barrow's inequality, and Oppenheim's inequality. Based on verification by computer, several related interesting conjectures are put forward. [ABSTRACT FROM AUTHOR]

Recently, some new sequence spaces ℓ p (A α) (0 < p < ∞) , c 0 (A α) , c (A α) , and ℓ ∞ (A α) have been studied by Yaying et al. (Forum Math., 2024, https://doi.org/10.1515/forum-2023-0138) as matrix domains of A α = (a n , v α) , where a m , v α = { v α ρ (α) (m) , v ∣ m , 0 , v ∤ m , and ρ (α) (m) : = sum of the α th power of the positive divisors of m ∈ N . They obtained their duals, matrix transformations and associated compact matrix operators for these matrix classes. This article deals with some geometric properties of these sequence spaces. [ABSTRACT FROM AUTHOR]

Recently, El-Deeb and Cotîrlă (Mathematics 11:11234834, 2023) used the error function together with a q-convolution to introduce a new operator. By means of this operator the following class R α , ϒ λ , q (δ , η) of analytic functions was studied: R α , ϒ λ , q (δ , η) : = { F : ℜ ((1 − δ + 2 η) H ϒ λ , q F (ζ) ζ + (δ − 2 η) (H ϒ λ , q F (ζ)) ′ + η ζ (H ϒ λ , q F (ζ)) ″) } > α (0 ≦ α < 1). For these general analytic functions F ∈ R β , ϒ λ , q (δ , η) , we give upper bounds for the Fekete–Szegö functional and for the second and third Hankel determinants. [ABSTRACT FROM AUTHOR]

The article presents a study which examines the theorem of the Brézis-Wainger inequality on a compact of Reimannian manifolds. It notes that the proof relies of a Moser-Trudinger inequality and the Sobolev embedding theorem. Moreover, it used the integral representation of a smooth function through the Green function. In order to make the paper more readable, researchers recalled some definitions and facts from the theory of Sobolev spaces on Reimannian manifolds. An overview of the proof of the study's theorem result is given.

This paper presents a new proof method about the paper (Yuan et al. in Appl. Math. Model. 47:811–825, 2017). In the proof, the global convergence of the Polak–Ribière–Polak algorithm is established without these two assumptions d k T g k < 0 and g k + 1 d k ≤ − σ 1 g k T d k which are needed in the above paper. This means that this paper has the same results under weaker conditions. More dimension functions for practical problems are tested to show the performance of the modified algorithm and the normal algorithm. An application of the fact engineering model is done to show the effectiveness of the given conjugate gradient algorithm. [ABSTRACT FROM AUTHOR]

The present investigation aims to examine the geometric properties of the normalized form of the combination of generalized Lommel–Wright function J λ , μ ν , m (z) : = Γ m (λ + 1) Γ (λ + μ + 1) 2 2 λ + μ z 1 − (ν / 2) − λ J λ , μ ν , m (z) , where the function J λ , μ ν , m satisfies the differential equation J λ , μ ν , m (z) : = (1 − 2 λ − ν) J λ , μ ν , m (z) + z (J λ , μ ν , m (z)) ′ with J ν , λ μ , m (z) = (z 2) 2 λ + ν ∑ k = 0 ∞ (− 1) k Γ m (k + λ + 1) Γ (k μ + ν + λ + 1) (z 2) 2 k for λ ∈ C ∖ Z − , Z − : = { − 1 , − 2 , − 3 , ... } , m ∈ N , ν ∈ C , and μ ∈ N 0 : = N ∪ { 0 } . In particular, we employ a new procedure using mathematical induction, as well as an estimate for the upper and lower bounds for the gamma function inspired by Li and Chen (J. Inequal. Pure Appl. Math. 8(1):28, 2007), to evaluate the starlikeness and convexity of order α, 0 ≤ α < 1 . Ultimately, we discuss the starlikeness and convexity of order zero for J λ , μ ν , m , and it turns out that they are useful to extend the range of validity for the parameter λ to λ ≥ 0 where the main concept of the proofs comes from some technical manipulations given by Mocanu (Libertas Math. 13:27–40, 1993). Our results improve, complement, and generalize some well-known (nonsharp) estimates. [ABSTRACT FROM AUTHOR]

This paper considers the problem of minimizing a nonlinear objective function subject to a system of bipolar fuzzy relational equations with max- $T_{L}$ composition, where $T_{L}$ is the Łukasiewicz triangular norm. It shows that the feasible domain, i.e., the solution set of a system of bipolar fuzzy relational equations, can be reformulated as a system of 0-1 mixed integer inequalities. Consequently, such a type of optimization problems can be handled within the framework of 0-1 mixed integer optimization requiring no particular solving techniques. [ABSTRACT FROM AUTHOR]

This paper addresses a novel solution scheme for a special class of variational inequality problems which can be applied to model a Stackelberg game with one leader and three or more followers. In the scheme, the leader makes his decision first and then the followers reveal their choices simultaneously based on the information of the leader's strategy. Under mild conditions, we theoretically prove that the scheme can obtain an equilibrium. The proposed approach is applied to solve a simple game and a traffic problem. Numerical results about the performance of the new method are reported. [ABSTRACT FROM AUTHOR]

In this paper, we investigate n-exponential convexity and log-convexity using the positive functional defined as the difference of the left-hand side and right-hand side of the inequality from (Pečarić and Janić in Facta Univ., Ser. Math. Inform. 3:39-42, ). We also give mean value theorems of Lagrange and Cauchy types. Finally, we construct means with Stolarsky property. [ABSTRACT FROM AUTHOR]

Based on the extreme value conditions of a multiple variables function, a new class of Wirtinger-type double integral inequality is established in this paper. The proposed inequality generalizes and refines the classical Wirtinger-based integral inequality and has less conservatism in comparison with Jensen’s double integral inequality and other double integral inequalities in the literature. Thus, the stability criteria for delayed control systems derived by the proposed refined Wirtinger-type integral inequality are less conservative than existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we use a result of Nunokawa to extend some results on univalent functions given by Miller and Mocanu. As a consequence, we get several sufficient conditions for starlikeness over the expression $f(z)f''(z)/f^{\prime2}(z)$. [ABSTRACT FROM AUTHOR]

In this paper, we look at the concept of multi- $C^{*}$-ternary algebras and consider some properties. As an application we approximate multi- $C^{*}$-ternary algebra homomorphisms and derivations in these spaces. [ABSTRACT FROM AUTHOR]

Recently, Lal (Appl. Math. Comput. 209:346-350, 2009) has determined the degree of approximation of a function belonging to Lip α and weighted [InlineEquation not available: see fulltext.]-classes using product [InlineEquation not available: see fulltext.] summability with non-increasing weights [InlineEquation not available: see fulltext.]. In this paper, we determine the degree of approximation of function [InlineEquation not available: see fulltext.], conjugate to a 2 π-periodic function f belonging to weighted [InlineEquation not available: see fulltext.]-class by dropping the monotonicity on the generating sequence [InlineEquation not available: see fulltext.] with a new (proper) set of conditions, which in turn generalizes the results of Mishra et al. (Bull. Math. Anal. Appl., 2013) on [InlineEquation not available: see fulltext.]-class and rectifies (removes) the errors of Mishra et al. (Mat. Vesn., 2013). Few examples and applications are also highlighted in this manuscript. MSC: Primary 42B05, 42B08, 40G05, 41A10. [ABSTRACT FROM AUTHOR]

In the paper, we solve one conjecture on an inequality involving digamma function, an open problem, and a conjecture on monotonicity of functions involving generalized digamma function. We also prove a new inequality for digamma function. [ABSTRACT FROM AUTHOR]

There are almost no results in mathematical literature on the exponential stability of third-order delay differential equations. One of the main purposes of the paper is to fill this gap. We propose an approach to the study of stability for third-order delay differential equations.On the basis of these results, new possibilities of stabilization by delay feedback input control are proposed. [ABSTRACT FROM AUTHOR]

Recently, we introduced a new coefficient as a generalization of the modulus of smoothness and Pythagorean modulus such as J , ( t). In this paper, We can compute the constant J , (1) under the absolute normalized norms on ℝ by means of their corresponding continuous convex functions on [0, 1]. Moreover, some sufficient conditions which imply uniform normal structure are presented. 2000 Mathematics Subject Classification: 46B20. [ABSTRACT FROM AUTHOR]

The article examines a perturbed Ostrowski-type inequality on time scales for k points for functions whose second derivatives are bounded. Authors of this paper have also point out some particular perturbed integral inequalities on time scales for functions whose second derivatives are bounded as special cases. These include perturbed rectangle inequality on time scales, perturbed trapezoid inequality on time scales, and perturbed mid-point inequality on time scales. The theory of time scales is considered as a theory capable to contain both difference and differential calculus in a consistent way.

The article provides an overview of the study which investigates the Jensen inequality for convex-concave antisymmetric functions and applications. It pointed out that a class of functions which is between of convex functions and the class of Jensen-convex functions is the class of Wright-convex functions. It presented several theorems which were the main motivations of the paper. It noted that it has proven that without loss of generality, it can suppose that (a,b) = (-1,1), thus, f is an odd function.

The article provides an overview of the study which examines the locally uniform nonsquare in generalized Cesàro sequence spaces. It found that the generalized Cesàro sequence spaces possessed the locally uniform nonsquare and have the fixed point property, but they are not uniformly nonsquare. It specified that the result is related to the result of the paper J. False and colleagues in 2006. It was done through giving examples and the motivation to find the geometric properties that are weaker than uniformly nonsquare, but still possessed the fixed point property in any Banach spaces .

The article provides an overview of a study which extends the paper on separately quasi-nearly subharmonic function by D. H. Armitage and S. J. Gardiner. With the aid of the extension, it obtained a slight refinement of Armitage and Gardiner's result in their classical case. It found that the method of proof has indicated a straightforward and technical, but still by no means, modification of Y. Domar's and Armitage and Gardiner's argument. Results of the refinement and calculations of the lemmas are also presented.

By using an integral arithmetic mean, a generalization of Levinson's inequality given in (Pečarić et al. in Convex Functions, Partial Orderings, and Statistical Applications. Mathematics in Science and Engineering, vol. 187, 1992) and results from (Vukelić in Appl. Anal. Discrete Math. 14:670–684, 2020), we give extension of Wulbert's result from (Wulbert in Math. Comput. Model. 37:1383–1391, 2003). Also, we obtain inequalities with divided differences for the functions of higher order. [ABSTRACT FROM AUTHOR]

This paper addresses approximately dual g-frames. First, we establish a connection between approximately dual g-frames and dual g-frames and obtain a characterization of approximately dual g-frames. Second, we give results on stability of approximately dual g-frames, which cover the results obtained by other authors. [ABSTRACT FROM AUTHOR]

In this paper we will establish a result by Connor, Khan and Orhan (Analysis 8:47–63, 1988; Publ. Math. (Debr.) 76:77–88, 2010) in the framework of the statistical convergence and the strong Cesàro convergence defined by a modulus function f. Namely, for every modulus function f, we will prove that a f-strongly Cesàro convergent sequence is always f-statistically convergent and uniformly integrable. The converse of this result is not true even for bounded sequences. We will characterize analytically the modulus functions f for which the converse is true. We will prove that these modulus functions are those for which the statistically convergent sequences are f-statistically convergent, that is, we show that Connor–Khan–Orhan's result is sharp in this sense. [ABSTRACT FROM AUTHOR]

In the present paper, we write out the eigenvalues and the corresponding eigenfunctions of the modified Frankl problem with a nonlocal oddness condition of the first kind in the Sobolev space $(W^{1}_{p}(0,\pi))$. We analyze the completeness, the basis property, and the minimality of the eigenfunctions in the space $(W^{1}_{p}(0,\pi))$. [ABSTRACT FROM AUTHOR]

In this paper we introduce new classes of p-bounded variation sequences and give a sufficient and necessary condition for weighted integrability of trigonometric series with coefficients belonging to these classes. This is a generalization of the results obtained by the first author [J. Inequal. Appl. 2010:1–19, 2010] and Dyachenko and Tikhonov [Stud. Math. 193(3):285–306, 2009]. [ABSTRACT FROM AUTHOR]

This research investigates bounds of the sum of left-sided and right-sided fractional integrals in a compact form. These bounds are established by using (α , m) -convex functions. The results of this paper also have connection with some known and already published results (Dragomir and Agarwal in Appl. Math. Lett. 11(5):91–95, 1998; Farid in J. Anal. 2018, https://doi.org/10.1007/s41478-0079-4; Farid et al. in Mathematics 2018(6):248, 2018). Moreover, the investigated results are applied to the end points as well as the mid point of the domain and some interesting consequences have been obtained. [ABSTRACT FROM AUTHOR]

In this paper, we present some new reverse arithmetic–geometric mean inequalities for operators and matrices due to Lin (Stud. Math. 215:187–194, 2013). Among other inequalities, we prove that if A , B ∈ B (H) are accretive and 0 < m I ≤ ℜ (A) , ℜ (B) ≤ M I , then, for every positive unital linear map Φ, Φ 2 (ℜ (A + B 2)) ≤ (K (h)) 2 Φ 2 (ℜ (A ♯ B)) , where K (h) = (h + 1) 2 4 h and h = M m . Moreover, some reverse harmonic–geometric mean inequalities are also presented. [ABSTRACT FROM AUTHOR]

The present paper deals with the limit behavior of iterates of Lupaş q- and (p,q)-Bernstein operators. We obtain the convergence for Lupaş q- and (p,q)-Bernstein operators by using the contraction principle. [ABSTRACT FROM AUTHOR]

In the present paper, we give the global Lq estimates for maximal operators generated by multiparameter oscillatory integral St,Φ, which is defined by St,Φf(x)=(2π)−n∫Rneix⋅ξei(t1ϕ1(|ξ1|)+t2ϕ2(|ξ2|)+⋯+tnϕn(|ξn|))fˆ(ξ)dξ,x∈Rn, where n≥2 and f is a Schwartz function in S(Rn), t=(t1,t2,...,tn), Φ=(ϕ1,ϕ2,...,ϕn), ϕi(i=1,2,3,...,n) is a function on R+→R, which has a suitable growth condition. These estimates are apparently good extensions to the results of Sjölin and Soria (J. Math. Anal. Appl 411:129-143, 2014) for the multiparameter fractional Schrödinger equation. [ABSTRACT FROM AUTHOR]

In this paper, we state and prove some new inequalities related to the rate of Lp approximation by Cesàro means of the quadratic partial sums of double Vilenkin-Fourier series of functions from Lp. [ABSTRACT FROM AUTHOR]

This paper deals with the first-order delayed differential systems {u′+a(t)u=h(t)v+f(t,u(t−τ(t))),v′+b(t)v=g(t,u(t−τ(t))), where a, b, τ, h are continuous ω-periodic functions with ∫0ωa(t)dt=0 and ∫0ωb(t)dt>0; f∈C(R×[0,∞),R) and g∈C(R×[0,∞),[0,∞)) are ω-periodic with respect to t. By means of the fixed point theorem in cones, several new existence theorems on positive periodic solutions are established. Our main results enrich and complement those available in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the central limit theorems for sub-linear expectation for a sequence of independent random variables without assumption of identical distribution. We first give a bound on the distance between the normalized sum distribution and G-normal distribution which can be used to derive the central limit theorem for sub-linear expectation under the Lindeberg condition. Then we obtain the central limit theorem for capacity under the Lindeberg condition. We also get the central limit theorem for capacity for summability methods under the Lindeberg condition. [ABSTRACT FROM AUTHOR]

The article investigates some delay integral inequalities on time scales which provide explicit bounds on unknown functions. Researchers have used Gronwall's inequality and comparison theorem. Results of the study unify and extend some delay integral inequalities and their corresponding discrete analogues. It was found that the numerical solution agrees with the analytical solution for some discrete inequalities. The inequalities given can be used as handy tools in the qualitative theory of certain classes of delay dynamic equations on time scales.

The article presents a study which investigates the cauchy functional inequality in Banach modules. It indicated that A be a unital C*-algebra with unitary group U(A) and unit e and assumed that X is a Banach A-module with norm ∥·[x] and that Y is a Banach A-module with norm ∥·[y]. It proved that the generalized Hyers-Ulam stability of A-linear mappings in Banach A-modules associated with the functional inequality. In addition, the computations in the proofs of the main theorems are specials cases of the general results obtained by G. L. Forti.

A personal narrative which explores the author's experience studying non linear integrals is presented.

The article establishes some geometric inequalities for a new Banach Sequence Space. It denotes the space whose elements are finite sets of distinct positive integers through the operator C. A space has been considered for matrix transformations. Some of its geometric properties are also considered. A Banach space is defined with a norm and a complete p-normed space with the p-norm. It examines the Banach-Saks property of type p, strict convexity and uniform convexity. It describes when a Banach space is said to have the Banach-Saks property of type p or property (BS) if every weakly null-sequence has a subsequence.