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In this paper, we propose an iterative algorithm, which is based on the Mann iterative method for solving simultaneously common fixed point problem with a finite family of demicontractive mappings and systems of variational inequalities involving an infinite family of strongly accretive operators. Under suitable assumptions, we prove the strong convergence of this algorithm in Banach spaces. Application to systems of constrained convex minimization problem is provided to support our main results. The results of this paper improve and extend results of [M. Eslamian, C. R. Math. Acad. Sci. Paris, 355 (2017), 1168–1177], and of many others. [ABSTRACT FROM AUTHOR]

Using Dotsonś convexity structure, the authors in [16, 17, 18] established some deterministic and random common fixed point results. In this note, we comment that the proofs of the results in [16, 17, 18] are incomplete and incorrect. [ABSTRACT FROM AUTHOR]

Abel et al. [U. Abel, M. Ivan, R. Pătănea, Appl. Math. Comput., 259 (2015), 116-123] introduced a Durrmeyer type integral variant of the Bernstein type operators based on two parameters defined by Stancu [D. D. Stancu, Calcolo, 35 (1998), 53-62]. Kajla [A. Kajla, Appl. Math. Comput., 316 (2018), 400-408] considered a Kantorovich modification of the Stancu operators wherein he studied some basic convergence theorems and also the rate of A-statistical convergence. In the present paper, we define a bivariate case of the operators proposed in [A. Kajla, Appl. Math. Comput., 316 (2018), 400-408] to study the degree of approximation for functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the complete modulus of continuity, the partial moduli of continuity and the Peetre's K-functional. Voronovskaya and Gr¨ uss Voronovskaya type theorems are also established. We introduce the associated GBS (Generalized Boolean Sum) operators of the bivariate operators and discuss the approximation degree of these operators with the aid of the mixed modulus of smoothness for B¨ogel continuous and Bögel differentiable functions. [ABSTRACT FROM AUTHOR]

this paper, we introduce the concept of generalized Suzuki type α-Z-contraction concerning a simulation function ζ in b-metric space and prove the existence of fixed point results for this contraction. Our result extend the fixed point result of [A. Padcharoen, P. Kumam, P. Saipara, P. Chaipunya, Kragujevac J. Math., 42 (2018), 419-430]. [ABSTRACT FROM AUTHOR]

In this paper we give a characterization for the uniform exponential stability of evolution families {Φ(t, t0)}t∞t0 on R+ that do not have an exponential growth, using the hypothesis that the pairs of function spaces (L∞(X);L∞(X)) and (Lp(X);Lq(X)), (p; q) 6= (∞;∞), are admissible to the evolution families. [ABSTRACT FROM AUTHOR]

In this paper, we define H(•;•)-η-cocoercive operators in q-uniformly smooth Banach spaces and its resolvent operator. We prove the Lipschitz continuity of the resolvent operator associated with H(•;•)-η-cocoercive operator and estimate its Lipschitz constant. By using the techniques of resolvent operator, an iterative algorithm for solving a variational-like inclusion problem is constructed. The existence of solution for the variational-like inclusions and the convergence of iterative sequences generated by the algorithm is proved. Some examples are given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a k-strict pseudo-contraction non-self mapping in Hilbert space. By the viscosity approximation algorithms, under suitable conditions , some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper extend and improve some recent results of Marino and Xu [G.Marino,H.K.Xu, Weak and strong convergence theorems for k-strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336-349], Zhou [H.Zhou, Convergence theorems of fixed Points for k-strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 69 (2008) 456-462], Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506- 515], Ceng,Homidan,etc [L. C. Ceng, S.A.Homidan, Q.H.Ansari, J. C. Yao, An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Comput. Appl. Math. 223 (2009) 967-974]. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of weak Weak θ-φ-contraction ensuring a convergence of successive approximations but does not force the mapping to be continuous at the fixed point. Thus, we answer one more solution to the open question raised by Rhoades in [B. E. Rhoades, Fixed point theory Appl, Berkeley, CA, (1986), Contemp. Math., Amer. Math. Soc., Providence, RI, 72 (1988), 233-245]. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce a new set-valued mapping by the scalar approximate solution mapping of a parametric generalized weak vector equilibrium problem and obtain some of its properties. By one of obtained properties, we establish the lower semicontinuity the approximate solution mapping to a parametric generalized weak vector equilibrium problem without the assumptions about monotonicity and approximate solution mappings. Simultaneously, under some suitable conditions, we obtain the upper semicontinuity of the approximate solution mapping to a generalized parametric weak vector equilibrium problem. Our main results improve and extend the corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some theorems about the Hyers-Ulam stability of the functional equation f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 2[f(2x) - 2f(x)] in paranormed spaces. From these theorems, as corollaries, we obtain the stability of the above functional equation with weaker conditions controlled by product of powers of norms and mixed-type product-sum of powers of norms. [ABSTRACT FROM AUTHOR]

We point out an error in the paper Shakeri [ J. Nonlinear Sci. Appl. 1 (2008), no. 3, 189-193]. [ABSTRACT FROM AUTHOR]

In this paper, one conjecture presented in the paper [V. Cîrtoaje, Proofs of Three Open Inequalities With Power-Exponential Functions, J. Nonlinear Sci. Appl. 4 (2011) no.2, 130-137, http://www.tjnsa.com] is proved. [ABSTRACT FROM AUTHOR]

In this paper, we give some Jensen-type inequalities for φ : I → R; I = [α,β] ⊂ R; where φ is a continuous function on I; twice di erentiable on I = (α,β) and there exists m = infφx∈I" (x) or M = supφx∈I" (x) : Furthermore, if φ'' is bounded on I ; then we give an estimate, from below and from above of Jensen inequalities. [ABSTRACT FROM AUTHOR]

In this paper, we define and study new strong convergence theorems of the modified Mann and the modified Ishikawa iterative scheme with errors for nonself-mappings which are total asymptotically nonexpansive in a uniformly convex Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we prove the weak and strong convergence of an explicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space. [ABSTRACT FROM AUTHOR]

In this paper using the notion of a sequentially dense monomorphism we consider sequential injectivity (s-injectivity) for acts over a semigroup S. We show that s-injectivity, s-absolutely retract, and sequential compactness are equivalent. [ABSTRACT FROM AUTHOR]

In this paper we generalize the notion of α-open and α-closed sets to ditopological texture spaces. We also introduce the concepts of α- bicontinuous difunctions and discuss their properties in detail. [ABSTRACT FROM AUTHOR]

Recently, Azam, Arshad and Beg introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we extend the Kannan's fixed point theorem in such spaces. [ABSTRACT FROM AUTHOR]

In this paper, we give a characteristic of B-convexity structures of finite dimensional B-spaces: if a finite dimensional B-space has the weak selection property then its B-convexity structure satisfies H-condition. We also get some relationships among B-convexity structures, selection property and fixed point property. We show that in a compact convex subset of a finite dimensional B-space satisfying H-condition the weak selection property implies the fixed point property. [ABSTRACT FROM AUTHOR]

In this paper we prove result for Jensen type mapping in the setting of intuitionistic fuzzy normed spaces. We generalize a Hyers-Ulam stability result in the framework of classical normed spaces. [ABSTRACT FROM AUTHOR]

In this paper we define the concept of finite and countable Cartesian products of PqpM-spaces and give a number of its properties. We also study the properties of topologies of those products. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of fuzzy Hilbert spaces and deduce the fuzzy version of Riesz representation theorem. Also we prove some results in fixed point theory and utilize the results to study the existence and uniqueness of solution of Uryson's integral equation. [ABSTRACT FROM AUTHOR]

In this paper, the notion of βS*-compactness is introduced in L-fuzzy topological spaces based on S*-compactness. A βS*-compactness L-fuzzy set is S*-compactness and also β-compactness. Some of its properties are discussed. We give some characterizations of βS*-compactness in terms of pre-open, regular open and semi-open L-fuzzy set. It is proved that βS*-compactness is a good extension of β-compactness in general topology. Also, we investigated the preservation theorems of βS*-compactness under some types of continuity. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following Neumann boundary value problem {-u″(x) = u3(x) - λ|u(x)|, x ϵ (0, 1), u′(0) = 0 = u′(1), where λ ϵ ℝ is parameter. We study the positive and negative solutions of this problem with respect to a parameter ρ (i.e. u(0) = ρ) in all ℝ*. By using a quadrature method, we obtain our results. Also we provide some details about the solutions that are obtained. [ABSTRACT FROM AUTHOR]

Let X be a Banach space and E be a closed bounded subset of X. For x ϵ X we set D(x,E) = sup{∥x - e∥ : e ϵ E}. The set E is called remotal in X if for any x ϵ X, there exists e ϵ E such that D(x,E) = ∥x - e∥ . It is the object of this paper to give new results on remotal sets in Lp(I,X), and to simplify the proofs of some results in [5]. [ABSTRACT FROM AUTHOR]

By combining the works of Moudafi [A. Moudafi, J. Math. Anal. Appl., 241 (2000), 46-55] and Iiduka and Takahashi [H. Iiduka, W. Takahashi, Nonlinear Anal., 61 (2005), 341-350], we introduce an iterative process that converges strongly to a particular solution of a variational inequality problem. We also study the stability of the algorithm under relatively small perturbation and we apply the obtained results to the study of a constrained optimization problem and a problem of common fixed points of two nonexpansive mappings. Some numerical experiments are provided to study the affect of some parameters on the speed of the convergence of the considered algorithm. [ABSTRACT FROM AUTHOR]

In the present paper, we prove common fixed point theorems using the notions of compatibility and subsequentially continuity (alternately subcompatibility and reciprocally continuity) in Menger spaces. We also give a common fixed point theorem satisfying an integral analogue. As applications to our results, we obtain the corresponding fixed point theorems in metric spaces. Some illustrative examples are also given which demonstrate the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper we will present an abstract point of view on iterative approximation schemes of fixed points for multivalued operators. More precisely, we suppose that the algorithms are convergent and we will study the impact of this hypothesis in the theory of operatorial inclusiosns: data dependence, stability and Gronwall type lemmas. Some open problems are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the general solution and we prove the generalized Hyers-Ulam stability for an affine functional equation. [ABSTRACT FROM AUTHOR]

Let X, Y be two nonempty sets and s, t : X → Y be two single-valued operators. By definition, a solution of the coincidence problem for s and t is a pair (x"; y") ∊ X ⨰ Y such that s(x"⨰) = t(x"⨰) = y⨰: It is well-known that a coincidence problem is, under appropriate conditions, equivalent to a fixed point problem for a single-valued operator generated by s and t. Using this approach, we will present some existence, uniqueness and Ulam - Hyers stability theorems for the coincidence problem mentioned above. Some examples illustrating the main results of the paper are also given. [ABSTRACT FROM AUTHOR]

In this paper, we present existence, uniqueness and Ulam-Hyers stability results for the coupled fiixed points of a pair of contractive type singlevalued and respectively multivalued operators on complete metric spaces. The approach is based on Perov type fixed point theorem for contractions in spaces endowed with vector- valued metrics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a fixed point theory for S-contractions in generalized Kasahara spaces (X, →, d), where d : X ⨰ X → s(R+) is not necessarily an s(R+)-metric. [ABSTRACT FROM AUTHOR]

A fixed point theorem for condensing maps due to Martelli combined with theories of a strongly continuous cosine family of bounded linear operators is used to investigate the existence of solutions to second order impulsive neutral functional integrodifferential inclusions with infinite delay in Banach spaces. [ABSTRACT FROM AUTHOR]

Existence of positive solution for a class of singular boundary value problems of the type -x″(t) = f(t, x(t), x′(t)), t ϵ (0, 1) x(0) = 0, x(1) = 0, is established. The nonlinearity f ϵ C((0, 1) × (0,1) × (-∞,∞), (-∞,∞)) is allowed to change sign and is singular at t = 0, t = 1 and/or x = 0. An example is included to show the applicability of our result. [ABSTRACT FROM AUTHOR]

This work is focused on the existence and attractivity of mild solutions for an integrodifferential system with statedependent delay. The results presented here were established by means of a fixed point theorem due to [T. A. Burton, C. Kirk, Math. Nachr., 189 (1998), 23-31]. At the end, the obtained results are illustrated by an example. [ABSTRACT FROM AUTHOR]

In this review article we present results regarding the fuzzy order relations. The concept of fuzzy order was introduced by generalizing the notion of re exivity, antisymmetric and transitivity. [ABSTRACT FROM AUTHOR]

Let fn(x; y; z) be a symmetric homogeneous polynomial of degree n = 4 or n = 6, in three real variables. We give necessary and sufficient conditions to have fn(x; y; z) ≥ 0 for all real numbers x; y; z. Then, we apply the obtained results to prove several relevant symmetric homogeneous polynomial inequalities of degree four and six. [ABSTRACT FROM AUTHOR]

The concepts of P-compactness, countable P-compactness, the P-Lindelöf property are introduced in L-topological spaces by means of preopen L-sets and their inequalities when L is a complete DeMorgan algebra. These definitions do not rely on the structure of the basis lattice L and no distributivity in L is required. They can also be characterized by means of preclosed L-sets and their inequalities. Their properties are researched. Further when L is a completely distributive DeMorgan algebra, their many characterizations are presented. [ABSTRACT FROM AUTHOR]

We are concerning with a nonlinear Hammerstein quadratic integral equation. We prove the existence of at least one positive solution x ϵ L1 under Carathèodory condition. Secondly we will make a link between Peano condition and Carathèodory condition to prove the existence of at least one positive continuous solution. Finally the existence of the maximal and minimal solutions will be proved. [ABSTRACT FROM AUTHOR]

We prove common fixed point theorems in symmetric spaces for two pairs of hybrid mappings using the concept of T-weakly and S-weakly commuting mappings satisfying generalized contractive conditions which generalize theorems of Aamri and El Moutawakil [J. Math. Anal. Appl., 270 (2002), 181-188.], Aamri and El Moutawakil [Appl. Math. E-notes., 3 (2003), 156-162.] and Aliouche [J. Math. Anal. Appl., 322 (2006), 796-802.]. [ABSTRACT FROM AUTHOR]

The concept of a generalized metric space, where the triangle inequality has been replaced by a more general one involving four points, has been recently introduced by Branciari. Subsequently, some classical metric fixed point theorems have been transferred to such a space. The aim of this note is to show that Kannan's fixed point theorem in a generalized metric space is a consequence of the Banach contraction principle in a metric space. [ABSTRACT FROM AUTHOR]

Using the method of explosive sub and supper solution, the existence and boundary behavior of positive boundary blow up solutions for some quasilinear elliptic systems with singular weight function are obtained under more extensive conditions. [ABSTRACT FROM AUTHOR]

We prove a related fixed point theorem for two mappings in two fuzzy metric spaces using an implicit relation which gives fuzzy versions of theorems of [1], [2] and [10]. [ABSTRACT FROM AUTHOR]