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In 2013, Azadifar et al. [3] established fixed point result in integral type contraction in modular metric space and 2020, Chaira et al.[11] established some extensions of Fixed Point Theorems for Weak-Contraction Mapping in Partially Ordered Modular Metric Spaces. In this paper we have established some common fixed point results in integral type contractions in modular and convex modular metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we look at the general form of the two-point quadrature formulas, which doesn't have to be symmetric. Under the convexity constraint of the first derivative, we propose a new scheme that gives the best approximation of the two-point quadrature rules. [ABSTRACT FROM AUTHOR]

This paper deals with the class S containing functions which are analytic and univalent in the open unit disc U = {z ∈ C: |z| < 1}. Functions f in S are normalized by f(0) = 0 and f′(0) = 1 and has the Taylor series expansion of the form f(z) = z + ∞X n=2 anzn. In this paper we investigate on the subclass of S of close-to-convex functions denoted as Cgα(λ, δ) where function f ∈ Cgα(λ, δ) satisfies Re{eiλ zf′(z) gα(z) } for |λ| < π 2, cos(λ) > δ, 0 ≤ δ < 1, 0 ≤ α ≤ 1 and gα = z (1-αz)2. The aim of the present paper is to find the upper bound of the Fekete-Szego functional |a3 - μa2 2| for the class Cgα(λ, δ). The results obtained in this paper is significant in the sense that it can be used in future research in this field, particularly in solving coefficient inequalities such as the Hankel determinant problems and also the Fekete-Szego problems for other subclasses of univalent functions. [ABSTRACT FROM AUTHOR]

This paper is concerned with certain generalized subclasses of multivalent quasi-convex functions defined with subordination. Various properties of these classes in regard to the coefficient estimates, distortion theorems, growth theorems, argument theorems and inclusion relations are discussed. Also, the relations with the earlier known results are established. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize the convexity preserving properties of sets by direct and inverse images initially stated for set-valued ratios of affine functions to a broader class of fractional type set-valued functions which strictly includes the first one. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of generalized convex functions called (h, r)-preinvex functions, and establish some new Hermite-Hadamard type inequalities under (h, r)-preinvexity. [ABSTRACT FROM AUTHOR]

In this paper, the authors established a new identity for differentiable functions, afterward, they obtained some new general inequalities for functions whose first derivatives in absolute value at certain powers are h-convex by using the identity. On the other hand, a general inequality is studied, which gives Hermite-Hadamard, Bullen and Simpson inequalities. Also, they gave some applications for special means for arbitrary positive numbers. [ABSTRACT FROM AUTHOR]

In this paper we establish some natural consequences of the Wirtinger integral inequality. Applications related to the trapezoid unweighted and weighted inequalities, of Fej'er's inequality for convex functions and of Gr¨uss' type inequalities are also provided. [ABSTRACT FROM AUTHOR]

In this paper, authors establish a new identity for a differentiable function using generic integral operators. By applying it, some new integral inequalities of trapezium, Ostrowski and Simpson type are obtained. Moreover, several special cases have been studied in detail. Finally, many useful applications have been found. [ABSTRACT FROM AUTHOR]

This paper is concerned with certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients ja2j and ja3j for the functions in these classes. Also we investigate upper bounds for the Fekete-Szego functional and second Hankel determinant for these classes. [ABSTRACT FROM AUTHOR]

In the present paper, we find certain results on Ruscheweyh operator using differential inequality. In particular, we find sufficient conditions for starlike and convex functions. [ABSTRACT FROM AUTHOR]

In this paper, the author establishes a new identity for differentiable func-tions and obtain some new inequalities for differentiable functions based on s-convexity, m-convexity and (,m)-convexity via Riemann-Liouville fractional integrals involving Gauss hypergeometric function. [ABSTRACT FROM AUTHOR]

In this paper, for a semi-infinite optimization Problem (P), second order - approximated optimization problems (P0,2), (P2,0), (P1,2), (P2,1) and (P2,2) are constructed. Some connections are established between the optimal solutions of these problems and optimal solutions of the original Problem (P). [ABSTRACT FROM AUTHOR]

The theory and applications of dynamic derivatives on time scales have recently received considerable interest. In this paper, we define a function using the combined diamond-α integral, investigate its monotonicity and give some refinements for Hölder's inequality. We present some applications for ℤ and ℝ. [ABSTRACT FROM AUTHOR]

In this paper, is defined the operator Dλ,ν,nα,β : A → A, given by Dλ,ν,nα,β f(z) = (1 - α - β)RνDnf(z) + αRνΩλzf(z) + βDnΩλzf(z), for z ∈ U, where Rν is the Ruscheweyh derivative, Dn is the Sălăgean operator, Ωλz is a fractional differintegral operator introduced by S. Owa and H. M. Srivastava, A = {f ∈ H(U) : f(z) = z + a2z² + a3z³ + ..., z ∈ U}, α, β ≥ 0, ν > -1, n ∈ N0 = {0, 1, 2, 3, ...}, -∞ < λ < 2. A certain subclass of analytic functions in the open unit disk, Rλ,ν,nα,β (δ), where 0 ≤ δ ≤ 1, is introduced using the new operator. Are obtained some properties of the class Rλ,ν,nα,β (δ) and some differential subordinations using the operator Dλ,ν,nα,β. [ABSTRACT FROM AUTHOR]

In this paper, we derive sufficient conditions for the univalence, starlikeness, convexity and some other properties in the class N (ρ), for a new integral operator defined on the space of normalized analytic functions in the open unit disk. [ABSTRACT FROM AUTHOR]

In this paper we establish some new general integral inequalities for twice differentiable functions. Then we apply these inequalities to obtain some inequalities for special means of real numbers. Finally, some new general quadrature rules of trapezoidal type are provided. [ABSTRACT FROM AUTHOR]

In this paper, we prove that Bernstein type Cheney and Sharma operators preserve modulus of continuity and Lipschitz continuity properties of the attached function f. We also introduce a result for these operators when f is a convex function. [ABSTRACT FROM AUTHOR]

In this paper we give a new generalized and sharpend version of Aczél- Popoviciu inequality via positive and homogeneous functionals. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class L(λ, μ, ϕ) of analytic functions f dened in the open unit disk U satisfying the subordination condition that q(z) Dλ+1f(z)/Dλf(z) ≺ ϕ(z) (λ ∈ N0; μ ≥ 0; z ∈ U); where q(z) = (z/Dλf(z))μ-2, Dλ is the Sλalλagean operator and ϕ(z) is a convex function with positive real part in U. We obtain some characteristic properties giving the coeficient inequality, radius and subordination results, and an inclusion result for the above class when the function ϕ(z) is a bilinear mapping in the open unit disk. For these functions f(z), sharp bounds for the initial coeficient and for the Fekete-Szego functional are determined, and also some integral representations are given. [ABSTRACT FROM AUTHOR]

In this paper we have introduced and studied the subclass RJ(d, α, β) of univalent functions defined by the linear operator RIγn,λ,lf(z) defined by using the Ruscheweyh derivative Rnf(z) and multiplier transformation I (n,λ,l) f(z), as RIγn,λ,l : A → A, RIγn,λ,lf(z) = (1-γ)Rnf(z) + γI (n,λ,l) f(z), zϵ U, where An = {fϵH(U) : f(z) = z+an+1zn+1+ . . . , z ϵ U} is the class of normalized analytic functions with A1 = A. The main object is to investigate several properties such as coefficient estimates, distortion theorems, closure theorems, neighborhoods and the radii of starlikeness, convexity and close-to-convexity of functions belonging to the class RJ(d, α, β). [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and investigate a new subclass χtp(γ) of analytic and p-valent close-to-convex functions in the open unit disk U. For functions belonging to the class χtp(γ), some interesting properties including the coefficient estimates, distortion theorems and subordination results are obtained. [ABSTRACT FROM AUTHOR]