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In the paper, the authors introduce a new notion "extended harmonically (s, m)-convex function" and establish some integral inequalities of the Hermite-Hadamard type for extended harmonically (s, m)-convex functions in terms of hypergeometric functions. [ABSTRACT FROM AUTHOR]

A new class of contraction pairs in uniformly convex metric spaces is introduced. The coincidence and best proximity points of this class of mappings is studied, and finally, illustrative examples are given to support the new results. [ABSTRACT FROM AUTHOR]

In this work, by using an integral identity together with both the Hölder and the Power-Mean integral inequality we establish several new inequalities for n-time differentiable r-convexand concave functions. [ABSTRACT FROM AUTHOR]

Some new Ostrowski's inequalities for functions whose nth derivatives are quasi-convex are established. [ABSTRACT FROM AUTHOR]

Some new inequalities of Fejér type for twice differentiable mappings are established via quantum calculus on finite intervals. The results presented are extensions of those given earlier. [ABSTRACT FROM AUTHOR]

The authors deduce a differentiable mapping integral identity with two parameters. Using this integral identity, this paper establishes new inequalities of Simpson type for extended ( s, m )-convex functions under certain conditions. This contributes to new better estimates than the earlier results. Finally, these inequalities are applied to special means. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we gain some basic properties and characterization theorems of the differential and local sub-differential of the fuzzy mapping, obtain an important result that the local sub-differential of fuzzy mapping is an empty set or a convex set. Secondly, we generalize the concept of local differentiability of fuzzy mapping, and obtain some basic properties about the concept. At last, we study the relationships between sub-differential of fuzzy mapping and differential of convex fuzzy mappings. Moreover, a sufficient condition that a class of fuzzy mapping have convex extension is gained. [ABSTRACT FROM AUTHOR]

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite–Hadamard–Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

Abstract: Connected with the celebrated Hermite–Hadamard integral inequality, several new inequalities for differentiable convex, wright-convex and quasi-convex mapping are established. Applications of these results are considered in error estimates for weighted Midpoint integral formula and in deriving the inequalities involving higher moments of random variables. [Copyright &y& Elsevier]

In this paper, we establish several new inequalities for some twice differantiable mappings. Then, we apply these inequalities to obtain new midpoint, trapezoid and perturbed trapezoid rules. Finally, some applications for special means of real numbers are provided. [ABSTRACT FROM AUTHOR]

Some new Hermite-Hadamard type inequalities are obtained for functions whose second derivatives absolute values are s-convex. [ABSTRACT FROM AUTHOR]

In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite–Hadamard integral inequality for mappings whose derivatives are $s$-$(\alpha , m)$-convex. The generalised integral inequalities contribute better estimates than some already presented. The inequalities are then applied to numerical integration and some special means. [ABSTRACT FROM AUTHOR]

A notion of quasi-regularity is extended for the inclusion problem $${F(p)\in C}$$ , where F is a differentiable mapping from a Riemannian manifold M to $${\mathbb R^n}$$ . When C is the set of minimum points of a convex real-valued function h on $${\mathbb R^n}$$ and D F satisfies the L-average Lipschitz condition, we use the majorizing function technique to establish the semi-local convergence of sequences generated by the Gauss-Newton method (with quasi-regular initial points) for the convex composite function h ◦ F on Riemannian manifold. Two applications are provided: one is for the case of regularities on Riemannian manifolds and the other is for the case when C is a cone and D F( p)(·) − C is surjective. In particular, the results obtained in this paper extend the corresponding one in Wang et al. (Taiwanese J Math 13:633-656, ). [ABSTRACT FROM AUTHOR]

We construct here an example of a continuous convex function on a locally convex space, which is MS-differentiable at a point, but is not HL-differentiable at this point. [ABSTRACT FROM AUTHOR]

Abstract: Several inequalities for differentiable convex, wright-convex and quasi-convex mapping are obtained respectively that are connected with the celebrated Hermite–Hadamard integral inequality. Also, some error estimates for weighted Trapezoid formula and higher moments of random variables are given. [Copyright &y& Elsevier]

Abstract: In this paper, we establish two inequalities for differentiable convex mappings and differentiable concave mappings which are connected with Fejér’s inequality holding for convex mappings and concave mappings. Some error estimates for the weighted trapezoidal formula and the weighted midpoint formula are given. [ABSTRACT FROM AUTHOR]

Abstract: It is well known that a (linear) operator between Banach spaces is completely continuous if and only if its adjoint takes bounded subsets of into uniformly completely continuous subsets, often called (L)-subsets, of . We give similar results for differentiable mappings. More precisely, if is an open convex subset, let be a differentiable mapping whose derivative is uniformly continuous on U-bounded subsets. We prove that f takes weak Cauchy U-bounded sequences into convergent sequences if and only if takes Rosenthal U-bounded subsets of U into uniformly completely continuous subsets of . As a consequence, we extend a result of P. Hájek and answer a question raised by R. Deville and E. Matheron. We derive differentiable characterizations of Banach spaces not containing and of Banach spaces without the Schur property containing a copy of . Analogous results are given for differentiable mappings taking weakly convergent U-bounded sequences into convergent sequences. Finally, we show that if X has the hereditary Dunford–Pettis property, then every differentiable function as above is locally weakly sequentially continuous. [Copyright &y& Elsevier]

Abstract: Based on the celebrated Hermite–Hadamard integral inequality for convex functions, some inequalities for differentiable convex and concave mappings are generalized. Furthermore, the results obtained are examined in the context of special means for real numbers. [Copyright &y& Elsevier]

Let be real Banach spaces. Let f(·) be a real-valued locally uniformly approximate convex function defined on an open subset . Let be an open subset. Let σ (·) be a differentiable mapping of ΩX into ΩY such that the differentials of are locally uniformly continuous function of x. Then f(σ (·)) is also a locally uniformly approximate convex function. Therefore the function f(σ (·)) is Fréchet differentiable on a dense Gδ-set, provided X is an Asplund space, and Gateaux differentiable on a dense Gδ-set, provided X is separable. As a consequence, we obtain that a locally uniformly approximate convex function defined on a -manifold is Fréchet differentiable on a dense Gδ-set, provided is an Asplund space, and Gateaux differentiable on a dense Gδ-set, provided E is separable. †Dedicated to Professor Diethard Pallaschke on the occasion of his 65th birthday. [ABSTRACT FROM AUTHOR]

Rockafellar proved that any closed, convex function is uniquely determined by its subdifferential mapping up to an additive constant. The aim of this article is to provide an elementary proof of the same result. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new Hermite-Hadamard inequality involving left-sided and right-sided ψ-Riemann-Liouville fractional integrals via convex functions. We also show two basic ψ-Riemann-Liouville fractional integral identities including the first order derivative of a given convex function, and these will be used to derive estimates for some fractional Hermite-Hadamard inequalities. Finally, we give some applications to special means of real numbers. [ABSTRACT FROM AUTHOR]

We investigate a weighted Simpson-type identity and obtain new estimation-type results related to the weighted Simpson-like type inequality for the first-order differentiable mappings. We also present some applications to f-divergence measures and to higher moments of continuous random variables. [ABSTRACT FROM AUTHOR]