• 제목/요약/키워드: conformable integral operators

검색결과 4건 처리시간 0.018초

BOUNDS OF AN INTEGRAL OPERATOR FOR CONVEX FUNCTIONS AND RESULTS IN FRACTIONAL CALCULUS

  • Mishira, Lakshmi Narayan;Farid, Ghulam;Bangash, Babar Khan
    • 호남수학학술지
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    • 제42권2호
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    • pp.359-376
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    • 2020
  • The present research investigates the bounds of an integral operator for convex functions and a differentiable function f such that |f'| is convex. Further, these bounds of integral operators specifically produce estimations of various classical fractional and recently defined conformable integral operators. These results also contain bounds of Hadamard type for symmetric convex functions.

ON OPIAL-TYPE INEQUALITIES VIA A NEW GENERALIZED INTEGRAL OPERATOR

  • Farid, Ghulam;Mehboob, Yasir
    • Korean Journal of Mathematics
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    • 제29권2호
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    • pp.227-237
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    • 2021
  • Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.

Reverse Inequalities through k-weighted Fractional Operators with Two Parameters

  • Bouharket Benaissa;Noureddine Azzouz
    • Kyungpook Mathematical Journal
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    • 제64권1호
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    • pp.31-46
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    • 2024
  • The aim of this paper is to present an approach to improve reverse Minkowski and Hölder-type inequalities using k-weighted fractional integral operators a+𝔍𝜇w with respect to a strictly increasing continuous function 𝜇, by introducing two parameters of integrability, p and q. For various choices of 𝜇 we get interesting special cases.

UNIFIED INTEGRAL OPERATOR INEQUALITIES VIA CONVEX COMPOSITION OF TWO FUNCTIONS

  • Mishra, Lakshmi Narayan;Farid, Ghulam;Mahreen, Kahkashan
    • Korean Journal of Mathematics
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    • 제29권1호
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    • pp.91-103
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    • 2021
  • In this paper we have established inequalities for a unified integral operator by using convexity of composition of two functions. The obtained results are directly connected to bounds of various fractional and conformable integral operators which are already known in literature. A generalized Hadamard integral inequality is obtained which further leads to its various versions for associated fractional integrals. Further, some implicated results are discussed.