On Extended Class of Totally Ordered Interval-Valued Convex Stochastic Processes and Applications
The intent of the current study is to explore convex stochastic processes within a broader context. We introduce the concept of unified stochastic processes to analyze both convex and non-convex stochastic processes simultaneously. We employ weighted quasi-mean, non-negative mapping <inline-formu...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-09-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/8/10/577 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850205138686312448 |
|---|---|
| author | Muhammad Zakria Javed Muhammad Uzair Awan Loredana Ciurdariu Silvestru Sever Dragomir Yahya Almalki |
| author_facet | Muhammad Zakria Javed Muhammad Uzair Awan Loredana Ciurdariu Silvestru Sever Dragomir Yahya Almalki |
| author_sort | Muhammad Zakria Javed |
| collection | DOAJ |
| description | The intent of the current study is to explore convex stochastic processes within a broader context. We introduce the concept of unified stochastic processes to analyze both convex and non-convex stochastic processes simultaneously. We employ weighted quasi-mean, non-negative mapping <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>, and center-radius ordering relations to establish a class of extended <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mi>r</mi></mrow></semantics></math></inline-formula>-interval-valued convex stochastic processes. This class yields a combination of innovative convex and non-convex stochastic processes. We characterize our class by illustrating its relationships with other classes as well as certain key attributes and sufficient conditions for this class of processes. Additionally, leveraging Riemann–Liouville stochastic fractional operators and our proposed class, we prove parametric fractional variants of Jensen’s inequality, Hermite–Hadamard’s inequality, Fejer’s inequality, and product Hermite–Hadamard’s like inequality. We establish an interesting relation between means by means of Hermite–Hadamard’s inequality. We utilize the numerical and graphical approaches to showcase the significance and effectiveness of primary findings. Also, the proposed results are powerful tools to evaluate the bounds for stochastic Riemann–Liouville fractional operators in different scenarios for a larger space of processes. |
| format | Article |
| id | doaj-art-bac5da086cf94254a4c3d20cb76336f8 |
| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-bac5da086cf94254a4c3d20cb76336f82025-08-20T02:11:09ZengMDPI AGFractal and Fractional2504-31102024-09-0181057710.3390/fractalfract8100577On Extended Class of Totally Ordered Interval-Valued Convex Stochastic Processes and ApplicationsMuhammad Zakria Javed0Muhammad Uzair Awan1Loredana Ciurdariu2Silvestru Sever Dragomir3Yahya Almalki4Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, PakistanDepartment of Mathematics, Government College University Faisalabad, Faisalabad 38000, PakistanDepartment of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, RomaniaDepartment of Mathematics, College of Engineering & Science, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, AustraliaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaThe intent of the current study is to explore convex stochastic processes within a broader context. We introduce the concept of unified stochastic processes to analyze both convex and non-convex stochastic processes simultaneously. We employ weighted quasi-mean, non-negative mapping <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>, and center-radius ordering relations to establish a class of extended <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mi>r</mi></mrow></semantics></math></inline-formula>-interval-valued convex stochastic processes. This class yields a combination of innovative convex and non-convex stochastic processes. We characterize our class by illustrating its relationships with other classes as well as certain key attributes and sufficient conditions for this class of processes. Additionally, leveraging Riemann–Liouville stochastic fractional operators and our proposed class, we prove parametric fractional variants of Jensen’s inequality, Hermite–Hadamard’s inequality, Fejer’s inequality, and product Hermite–Hadamard’s like inequality. We establish an interesting relation between means by means of Hermite–Hadamard’s inequality. We utilize the numerical and graphical approaches to showcase the significance and effectiveness of primary findings. Also, the proposed results are powerful tools to evaluate the bounds for stochastic Riemann–Liouville fractional operators in different scenarios for a larger space of processes.https://www.mdpi.com/2504-3110/8/10/577convex mappingstochastic processesinterval-valuedcenter-radius orderingRiemann–Liouville fractional operator |
| spellingShingle | Muhammad Zakria Javed Muhammad Uzair Awan Loredana Ciurdariu Silvestru Sever Dragomir Yahya Almalki On Extended Class of Totally Ordered Interval-Valued Convex Stochastic Processes and Applications Fractal and Fractional convex mapping stochastic processes interval-valued center-radius ordering Riemann–Liouville fractional operator |
| title | On Extended Class of Totally Ordered Interval-Valued Convex Stochastic Processes and Applications |
| title_full | On Extended Class of Totally Ordered Interval-Valued Convex Stochastic Processes and Applications |
| title_fullStr | On Extended Class of Totally Ordered Interval-Valued Convex Stochastic Processes and Applications |
| title_full_unstemmed | On Extended Class of Totally Ordered Interval-Valued Convex Stochastic Processes and Applications |
| title_short | On Extended Class of Totally Ordered Interval-Valued Convex Stochastic Processes and Applications |
| title_sort | on extended class of totally ordered interval valued convex stochastic processes and applications |
| topic | convex mapping stochastic processes interval-valued center-radius ordering Riemann–Liouville fractional operator |
| url | https://www.mdpi.com/2504-3110/8/10/577 |
| work_keys_str_mv | AT muhammadzakriajaved onextendedclassoftotallyorderedintervalvaluedconvexstochasticprocessesandapplications AT muhammaduzairawan onextendedclassoftotallyorderedintervalvaluedconvexstochasticprocessesandapplications AT loredanaciurdariu onextendedclassoftotallyorderedintervalvaluedconvexstochasticprocessesandapplications AT silvestruseverdragomir onextendedclassoftotallyorderedintervalvaluedconvexstochasticprocessesandapplications AT yahyaalmalki onextendedclassoftotallyorderedintervalvaluedconvexstochasticprocessesandapplications |