scholarly journals Mean Square Integral Inequalities for Generalized Convex Stochastic Processes via Beta Function

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Putian Yang ◽  
Shiqing Zhang
Keyword(s):  
Applied Sciences ◽  
Stochastic Processes ◽  
Beta Function ◽  
Integral Inequalities ◽  
Mean Square ◽  
Convex Stochastic Processes

The integral inequalities have become a very popular area of research in recent years. The present paper deals with some important generalizations of convex stochastic processes. Several mean square integral inequalities are derived for this generalization. The involvement of the beta function in the results makes the inequalities more convenient for applied sciences.

scholarly journals Quantum Hermite-Hadamard type integral inequalities for convex stochastic processes

2021 ◽  
Vol 6 (11) ◽  
pp. 11989-12010
Author(s):  
Thanin Sitthiwirattham ◽  
◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Saowaluck Chasreechai ◽  
...  
Keyword(s):  
Stochastic Processes ◽  
Integral Inequalities ◽  
Mean Square ◽  
Type Integral ◽  
Convex Stochastic Processes

<abstract><p>In this paper, we introduce the notions of $ q $-mean square integral for stochastic processes and co-ordinated stochastic processes. Furthermore, we establish some new quantum Hermite-Hadamard type inequalities for convex stochastic processes and co-ordinated stochastic processes via newly defined integrals. It is also revealed that the results presented in this research transformed into some already proved results by considering the limits as $ q, \; q_{1}, \; q_{2}\rightarrow 1^{-} $ in the newly obtained results.</p></abstract>

scholarly journals Hermite-Hadamard, Jensen, and Fractional Integral Inequalities for Generalized P -Convex Stochastic Processes

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Fangfang Ma ◽  
Waqas Nazeer ◽  
Mamoona Ghafoor
Keyword(s):  
Probability Theory ◽  
Convex Function ◽  
Stochastic Processes ◽  
Fractional Integral ◽  
Probabilistic Models ◽  
Random Variable ◽  
Expected Value ◽  
Integral Inequalities ◽  
Stochastic Convexity ◽  
Convex Stochastic Processes

The stochastic process is one of the important branches of probability theory which deals with probabilistic models that evolve over time. It starts with probability postulates and includes a captivating arrangement of conclusions from those postulates. In probability theory, a convex function applied on the expected value of a random variable is always bounded above by the expected value of the convex function of that random variable. The purpose of this note is to introduce the class of generalized p -convex stochastic processes. Some well-known results of generalized p -convex functions such as Hermite-Hadamard, Jensen, and fractional integral inequalities are extended for generalized p -stochastic convexity.

scholarly journals Hermite-Hadamard type inequalities for p-convex stochastic processes

2019 ◽  
Vol 9 (2) ◽  
pp. 148-153 ◽  
Author(s):  
Nurgul Okur ◽  
Imdat Işcan ◽  
Emine Yuksek Dizdar
Keyword(s):  
Stochastic Process ◽  
Mathematical Programming ◽  
Stochastic Processes ◽  
Mean Square ◽  
Important Place ◽  
Mathematical Programming Problems ◽  
Square Integrability ◽  
Convex Stochastic Processes ◽  
Convex Stochastic Process

In this study are investigated p-convex stochastic processes which are extensions of convex stochastic processes. A suitable example is also given for this process. In addition, in this case a p-convex stochastic process is increasing or decreasing, the relation with convexity is revealed. The concept of inequality as convexity has an important place in literature, since it provides a broader setting to study the optimization and mathematical programming problems. Therefore, Hermite-Hadamard type inequalities for p-convex stochastic processes and some boundaries for these inequalities are obtained in present study. It is used the concept of mean-square integrability for stochastic processes to obtain the above mentioned results.

scholarly journals Multidimensional general convexity for stochastic processes and associated with Hermite-Hadamard type integral inequalities

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1971-1979 ◽  
Author(s):  
Nurgul Okur
Keyword(s):  
Stochastic Processes ◽  
Integral Inequalities ◽  
Type Integral ◽  
General Convex ◽  
General Convexity ◽  
Convex Stochastic Processes

In this study, we idetified multidimensional general convex stochastic processes. Concordantly, we obtained some important results related stochastic processes. Moreover, we derived some Hermite-Hadamard type integral inequalities for these stochastic processes.

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