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DOI: 10.23952/jnfa.2024.25
Received May 13, 2024; Accepted October 30, 2024; Published November 29, 2024
Abstract. Recently, there has been growing interest among researchers in extending and generalizing the concept of convexity to incorporate fractional theory and related inequalities. One notable extension which involves studying convexity on fractal sets is the (h-m)-convexity, which generalizes the h-convexity and m-convexity concepts. In this paper, we present a new notion of generalized (h-m)-preinvex functions, which is a generalization of convexity on fractal sets, along with various characteristics for the newly presented functions. Utilizing the new concept, we derive new Hermite-Hadamard-type inequalities and establish a new identity for generalized (h-m)-preinvex functions with parameters involving local fractional integrals. In addition, we derive some general local fractional integral inequalities for generalized (h-m)-preinvex functions. We utilize our findings in practical applications by selecting particular values for the variables to construct various generalizations of midpoint, trapezoidal, and Simpson type inequalities. The findings of this work provide essential extensions and generalizations of earlier studies conducted in the area.
How to Cite this Article:
S. Al-Sa’di, M. Bibi, Y. Seol, M. Muddassar, (h-m)-preinvex functions on fractal sets and local fractional integral inequalities with applications, J. Nonlinear Funct. Anal. 2024 (2024) 25.