scholarly journals Boundedness of generalized fractional integral operators on Orlicz spaces near $L^1$ over metric measure spaces

2018 ◽  
Vol 69 (1) ◽  
pp. 207-223
Author(s):  
Daiki Hashimoto ◽  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Fractional Integral ◽  
Orlicz Spaces ◽  
Integral Operators ◽  
Metric Measure Spaces ◽  
Fractional Integral Operators ◽  
Measure Spaces ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces

2018 ◽  
Vol 25 (2) ◽  
pp. 303-311
Author(s):  
Yoshihiro Sawano ◽  
Tetsu Shimomura
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Transforms ◽  
Morrey Spaces ◽  
Metric Measure Spaces ◽  
Fractional Integral Operators ◽  
Generalized Morrey Spaces ◽  
Measure Spaces ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

Abstract In this paper, we aim to deal with the boundedness and the weak-type boundedness for the generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces, as an extension of [Y. Sawano and T. Shimomura, Boundedness of the generalized fractional integral operators on generalized Morrey spaces over metric measure spaces, Z. Anal. Anwend. 36 2017, 2, 159–190], [Y. Sawano and T. Shimomura, Generalized fractional integral operators over non-doubling metric measure spaces, Integral Transforms Spec. Funct. 28 2017, 7, 534–546] and [I. Sihwaningrum, H. Gunawan and E. Nakai, Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces, Math. Nachr., to appear].

scholarly journals On Extended General Mittag–Leffler Functions and Certain Inequalities

2019 ◽  
Vol 3 (2) ◽  
pp. 32
Author(s):  
Marcela V. Mihai ◽  
Muhammad Uzair Awan ◽  
Muhammad Aslam Noor ◽  
Tingsong Du ◽  
Artion Kashuri ◽  
...  
Keyword(s):  
Convex Functions ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Function Of Two Variables ◽  
Generalized Fractional Integral Operators

In this paper, we introduce and investigate generalized fractional integral operators containing the new generalized Mittag–Leffler function of two variables. We establish several new refinements of Hermite–Hadamard-like inequalities via co-ordinated convex functions.

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