7 documents found, page 1 of 1
New quantum integral inequalities for left and right log-ℏ-convex interval-valu...
Cheng, Haiyang; Zhao, Dafang; Zhao, Guohui; Torres, Delfim F. M.We introduce the concept of quantum integration for interval-valued functions and establish new q-Hermite–Hadamard and q-Hermite–Hadamard–Fejér inequalities for left and right log-h -convex interval-valued functions. Our results generalize the known ones in the literature and serve as a foundation for future studies in inequalities for interval-valued functions and interval differential equations. We illustrate...
Quantum Hermite-Hadamard type inequalities for interval-valued functions
Cheng, Haiyang; Zhao, Dafang; Zhao, Guohui; Torres, Delfim F. M.We introduce the concept of quantum integration for interval-valued functions, and establish new q-Hermite-Hadamard and q-Hermite-Hadamard-Fejér inequalities for left and right h-convex interval-valued functions. The findings generalize known results in the literature and serve as a foundation for future studies in inequalities for interval-valued functions and interval differential equations. The results are ill...
Discrete Opial type inequalities for interval-valued functions
Zhao, Dafang; You, Xuexiao; Torres, Delfim F. M.We introduce the forward (backward) gH-difference operator of interval sequences, and establish some new discrete Opial type inequalities for interval-valued functions. Further, we obtain generalizations of classical discrete Opial type inequalities. Some examples are presented to illustrate our results.
Some inequalities for interval-valued functions on time scales
Zhao, Dafang; Ye, Guoju; Liu, Wei; Torres, Delfim F. M.We introduce the interval Darboux delta integral (shortly, the IDΔ -integral) and the interval Riemann delta integral (shortly, the IR Δ -integral) for interval-valued functions on time scales. Fundamental properties of ID and IR Δ -integrals and examples are given. Finally, we prove Jensen’s, Hölder’s and Minkowski’s inequalities for the IR Δ -integral. Also, some examples are given to illustrate our theorems
Existence theorems for a nonlinear second-order distributional differential equ...
Liu, Wei; Ye, Guoju; Zhao, Dafang; Torres, Delfim F. M.In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is based on the Leray--Schauder nonlinear alternative and Kurzweil--Henstock--Stieltjes integrals. Meanwhile, examples are worked out to demonstrate that the main results are s...
The fuzzy Henstock–Kurzweil delta integral on time scales
Zhao, Dafang; Ye, Guoju; Liu, Wei; Torres, Delfim F. M.We investigate properties of the fuzzy Henstock–Kurzweil delta integral (shortly, FHK Δ -integral) on time scales, and obtain two necessary and sufficient conditions for FHK Δ -integrability. The concept of uniformly FHK Δ -integrability is introduced. Under this concept, we obtain a uniformly integrability convergence theorem. Finally, we prove monotone and dominated convergence theorems for the FHK Δ -integral.
On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales
You, Xuexiao; Zhao, Dafang; Torres, Delfim F. M.We introduce and investigate the Henstock-Kurzweil (HK) integral for Riesz-space-valued functions on time scales. Some basic properties of the HK delta integral for Riesz-space-valued functions are proved. Further, we prove uniform and monotone convergence theorems.