Bi-additive s-functional inequalities and biderivation in modular spaces

In this paper,there are new considerations about the dual of a modular spaces and weak convergence. Two common fixed point theorems for a -non-expansive mapping defined on a star-shaped weakly compact subset are proved, Here the conditions of affineness, demi-closedness and Opial's property play an active role in the proving our results.

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Stability of a generalized n-variable mixed-type functional equation in fuzzy modular spaces

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02594-y ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Murali Ramdoss ◽

Divyakumari Pachaiyappan ◽

Choonkil Park ◽

Jung Rye Lee

Keyword(s):

Functional Equation ◽

Fixed Point ◽

General Solution ◽

Functional Equations ◽

Mixed Type ◽

Research Paper ◽

Fixed Point Method ◽

Quadratic Functional ◽

Ulam Stability ◽

Modular Spaces

AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

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Functional Inequalities for Two-Level Concentration

Potential Analysis ◽

10.1007/s11118-021-09900-9 ◽

2021 ◽

Author(s):

Franck Barthe ◽

Michał Strzelecki

Keyword(s):

Sobolev Inequality ◽

Poincaré Inequality ◽

Logarithmic Sobolev Inequality ◽

Probability Measures ◽

Exponential Rate ◽

Functional Inequalities ◽

Concentration Inequality ◽

Poincare Inequality ◽

Free Concentration ◽

Concentration Property

AbstractProbability measures satisfying a Poincaré inequality are known to enjoy a dimension-free concentration inequality with exponential rate. A celebrated result of Bobkov and Ledoux shows that a Poincaré inequality automatically implies a modified logarithmic Sobolev inequality. As a consequence the Poincaré inequality ensures a stronger dimension-free concentration property, known as two-level concentration. We show that a similar phenomenon occurs for the Latała–Oleszkiewicz inequalities, which were devised to uncover dimension-free concentration with rate between exponential and Gaussian. Motivated by the search for counterexamples to related questions, we also develop analytic techniques to study functional inequalities for probability measures on the line with wild potentials.

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PROBABILISTIC MODULAR SPACES

Further Progress in Analysis ◽

10.1142/9789812837332_0077 ◽

2009 ◽

Author(s):

K. NOUROUZI

Keyword(s):

Modular Spaces

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On a certain stability of the Hermite–Hadamard inequality

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2008.0291 ◽

2008 ◽

Vol 465 (2102) ◽

pp. 571-583 ◽

Cited By ~ 5

Author(s):

Attila Házy ◽

Zsolt Páles

Keyword(s):

Functional Inequalities ◽

Hadamard Inequality ◽

Real Functions ◽

The Stability

The classical Hermite–Hadamard inequality, under some regularity assumptions, characterizes convexity of real functions. The aim of this paper is to establish connections between the stability forms of the functional inequalities related to Jensen convexity, convexity and the Hermite–Hadamard inequality.

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