Hermite-Hadamard type inequality for operator preinvex functions

Ghazanfari, A. G.; Shakoori, Mahmood; Barani, A.; Dragomir, Sever S

doi:10.48550/arxiv.1306.0730

Cited by 1 publication

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 1. (see [3], Theorem 3) Let Ê be an invex subset of B( Ê) + sa and let be a function, where : Ê × Ê → B( Ê) + sa and g1 : I ⊆ R 0 → R is a continuous function on the interval I. Suppose also that the set Ê satisfies the condition ( Ĉ) on the set Ê.…”

Section: Definitionmentioning

confidence: 99%

“…Researchers working on these two famous inequalities have obtained generalizations, extensions, improvements, and iterations by considering different types of convex functions, different types of derivative and integral operators, new methods, and different spaces. Hermite-Hadamard inequalities for operator convex and generalized convex functions have proposed (see, for example [2][3][4][5][6][7]). In 2015, Barani [8] developed the Hermite-Hadamard inequalities for the products of two operator preinvex functions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fejér-Type Midpoint and Trapezoidal Inequalities for the Operator ω1,ω2-Preinvex Functions

Mehmood

Srivástava

Mohammed

et al. 2022

Axioms

View full text Add to dashboard Cite

In this work, we obtain some new integral inequalities of the Hermite–Hadamard–Fejér type for operator ω1,ω2-preinvex functions. The bounds for both left-hand and right-hand sides of the integral inequality are established for operator ω1,ω2-preinvex functions of the positive self-adjoint operator in the complex Hilbert spaces. We give the special cases to our results; thus, the established results are generalizations of earlier work. In the last section, we give applications for synchronous (asynchronous) functions.

show abstract

Section: Definitionmentioning

confidence: 99%