Notions of generalized \(s\)-convex functions on fractal sets

DOI10.1186/s13660-015-0826-xzbMath1336.26010OpenAlexW1878590305WikidataQ59428250 ScholiaQ59428250MaRDI QIDQ262558

Adem Kilicman, Wedad Saleh

Publication date: 30 March 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-015-0826-x

zbMATH Keywords

\(s\)-convex functionsfractal spacelocal fractional derivative

Mathematics Subject Classification ID

Inequalities for sums, series and integrals (26D15) Convexity of real functions in one variable, generalizations (26A51) Inequalities involving other types of functions (26D07)

Related Items

Some new local fractional inequalities associated with generalized \((s,m)\)-convex functions and applications ⋮ Generalized trapezium-type inequalities in the settings of fractal sets for functions having generalized convexity property ⋮ On new generalized unified bounds via generalized exponentially harmonically \(s\)-convex functions on fractal sets ⋮ Generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized \(s\)-convex in the second sense ⋮ EXACT TRAVELING-WAVE SOLUTIONS FOR ONE-DIMENSIONAL MODIFIED KORTEWEG–DE VRIES EQUATION DEFINED ON CANTOR SETS ⋮ CERTAIN INTEGRAL INEQUALITIES CONSIDERING GENERALIZED m-CONVEXITY ON FRACTAL SETS AND THEIR APPLICATIONS ⋮ New integral inequalities for \(s\)-convex functions of the second sense via the Caputo fractional derivative and the Caputo-Fabrizio integral operator ⋮ The Popoviciu type inequalities for s-convex functions in the third sense ⋮ On some inequalities for generalized s-convex functions and applications on fractal sets ⋮ Advanced analysis of local fractional calculus applied to the Rice theory in fractal fracture mechanics ⋮ A new computational approach for solving nonlinear local fractional PDEs ⋮ Unnamed Item ⋮ NEW COMPUTATIONS OF OSTROWSKI-TYPE INEQUALITY PERTAINING TO FRACTAL STYLE WITH APPLICATIONS

Cites Work

• Local fractional similarity solution for the diffusion equation defined on Cantor sets
• Generalized \(s\)-convex functions on fractal sets
• Generalized convex functions on fractal sets and two related inequalities
• Application of the local fractional series expansion method and the variational iteration method to the Helmholtz equation involving local fractional derivative operators
• Approximation solutions for local fractional Schrödinger equation in the one-dimensional Cantorian system
• Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis
• ON GENERALIZED s-CONVEX FUNCTIONS ON FRACTAL SETS
• Notions of convexity
• Static-kinematic duality and the principle of virtual work in the mechanics of fractal media
• Unnamed Item
• Unnamed Item