New Generalizations of Ostrowski-Like Type Inequalities for Fractional Integrals

Abstract

Abstract. In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.

SOME NEW OSTROWSKI TYPE INEQUALITIES FOR GENERALIZED (s, m, ϕ)-PREINVEX FUNCTIONS VIA FRACTIONAL INTEGRAL OPERATORS

“…In Section 4, some conclusions and future research are given. These results not only extend the results appeared in the literature (see [1]) but also provide new estimates on these type.…”

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In the present paper, the notion of generalized (s, m, ϕ)-preinvex function is applied to establish some new generalizations of Ostrowski type inequalities via fractional integral operators. These results not only extend the results appeared in the literature (see [1]) but also provide new estimates on these type. Some applications to special means are also given.

Mathematics Subject Classification.Primary: 26A51; Secondary: 26A33, 26D07, 26D10, 26D15.Key words and phrases.

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“…Corollary 5. If we choose σ(0) = 1, w = 0 in Corollary 4, the inequality (2.9) reduces to inequality (2.4) of (see [1] Theorem 2.3).…”

SOME NEW OSTROWSKI TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR BETA (r, g)-PREINVEX FUNCTIONS VIA CAPUTO k-FRACTIONAL DERIVATIVES,

“…For other recent results concerning Ostrowski type inequalities readers are related to, see [5], [15], [17], [20], [24], [27]- [29], [31], [36]- [39]. Ostrowski inequality is playing a very important role in all the fields of mathematics, especially in the theory of approximations.…”

Ostrowski Type Inequalities Pertaining Strongly Convex Functions Via Conformable Fractional Integrals and Their Applications

“…Ostrowski inequality is playing a very important role in all the fields of mathematics, especially in the theory of approximations. Thus such inequalities were studied extensively by many researches and numerous generalizations, extensions, variants and applications can be found in the literature [ [1]- [4], [7]- [13], [15], [16], [18]- [20], [23]- [27], [29], [30]].…”