New Inequalities for Ah-Convex Functions Using Beta and Hypergeometric Functions

Kadakal, Huriye; Bekar, Kerim

doi:10.46753/pjaa.2019.v06i02.004

Cited by 4 publications

(1 citation statement)

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“…Ahmad et al [14] created a fractional variation of the H-H-type inequality by combining fractional integrals with exponential kernels. For more recent developments on this topic, see Khan et al [15], Marinescu and Monea [16], şcan [17], Kadakal et al [18], and Kadakal and Bekar [19], as well as [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels

et al. 2023

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The concept of convexity is fundamental in order to produce various types of inequalities. Thus, convexity and integral inequality are closely related. The objectives of this paper are to present a new class of up and down convex fuzzy number valued functions known as up and down exponential trigonometric convex fuzzy number valued mappings (UDET-convex FNVMs) and, with the help of this newly defined class, Hermite–Hadamard-type inequalities (H–Htype inequalities) via fuzzy inclusion relation and fuzzy fractional integral operators having exponential kernels. This fuzzy inclusion relation is level-wise defined by the interval-based inclusion relation. Furthermore, we have shown that our findings apply to a significant class of both novel and well-known inequalities for UDET-convex FNVMs. The application of the theory developed in this study is illustrated with useful instances. Some very interesting examples are provided to discuss the validation of our main results. These results and other approaches may open up new avenues for modeling, interval-valued functions, and fuzzy optimization problems.

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Section: Introductionmentioning

confidence: 99%

Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels

et al. 2023

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On the fractional integral inclusions having exponential kernels for interval-valued convex functions

Zhou

Yuan

2021

Math Sci

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Research on New Interval-Valued Fractional Integrals with Exponential Kernel and Their Applications

Aljohani,

Althobaiti,

Althobaiti

2024

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This paper aims to introduce a new fractional extension of the interval Hermite–Hadamard (HH), HH–Fejér, and Pachpatte-type inequalities for left- and right-interval-valued harmonically convex mappings (LRIVH convex mappings) with an exponential function in the kernel. We use fractional operators to develop several generalizations, capturing unique outcomes that are currently under investigation, while also introducing a new operator. Generally, we propose two methods that, in conjunction with more generalized fractional integral operators with an exponential function in the kernel, can address certain novel generalizations of increasing mappings under the assumption of LRIV convexity, yielding some noteworthy results. The results produced by applying the suggested scheme show that the computational effects are extremely accurate, flexible, efficient, and simple to implement in order to explore the path of upcoming intricate waveform and circuit theory research.

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New Inequalities for Ah-Convex Functions Using Beta and Hypergeometric Functions

Cited by 4 publications

References 0 publications

Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels

Some New Properties of Exponential Trigonometric Convex Functions Using up and down Relations over Fuzzy Numbers and Related Inequalities through Fuzzy Fractional Integral Operators Having Exponential Kernels

On the fractional integral inclusions having exponential kernels for interval-valued convex functions

Research on New Interval-Valued Fractional Integrals with Exponential Kernel and Their Applications

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