**Thai Journal of Mathematics (TJM)**is a peer-reviewed, open access international journal publishing original research works of high standard in all areas of pure and applied mathematics.

**Publication Frequency**

TJM publishes one volume per year. Usually a volume consists of three issues with about 200-400 pages each.

*March*,

*June*,

*September,*and

*December*). All manuscripts are refereed under the same standards as those used by the finest-quality printed mathematical journals. Accepted papers will be published online in their final forms using the TJM template and will be published in four issues annually.

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**Article Processing Charge**

**Foreign**

- 550 USD

**Domestic**

- University cepmart members 7,000 THB

- University non-cepmart members 10,000 THB

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**Reviewing/Indexing**

**is covered Abstracted, Reviewed and Indexeded in:**

Thai J Math.

Thai J Math.

**Mathematical Reviews**,

**MathSciNet**,

**Zentralblatt MATH Database**,

**Google Scholar**and

**Scopus [Elsevier]**

**Thomson Reuters**).

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**Call for Papers: ***Thai Journal of Mathematics (TJM) **is pleased to announce the call for papers for the following special issues:*

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**Special Issue: Discrete and Computational Geometry, Graphs, and Games**

This special issue is dedicated to the topics of the recent conference held online on September 3-5, 2021: *Thailand-Japan Conference on Discrete and Computational Geometry, Graphs, and Games* (TJCDCG^3 2020+1).

- Discrete Geometry,
- Computational Geometry,
- Graph Theory,
- Graph Algorithms,
- Complexity,
- Winning Strategies of Games and Puzzles.

**Instruction for Authors:**Please follow the instructions for authors by the following link:

http://thaijmath.in.cmu.ac.th/index.php/thaijmath/about/submissions#onlineSubmissions

**Submission Deadline: **The submission deadline is postponed from the information announced in the conference. The new submission deadline is January 31, 2022.

**Guest Editors:**Guest co-Editor:

- Hiro ITO (The Univ. of Electro-Communications),
- Toshinori SAKAI (Tokai Univ.),
- Wanida HEMAKUL (Chulalongkorn University).

Managing Editor: Supanut CHAIDEE (Chiang Mai University).

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**Special Issue: Memory of Professor Charles E. Chidume**

**Brief:**Professor Charles E. Chidume was born on the 11th of August, 1947. He passed away on the 7th of October, 2021 at the age of 74, after a brief illness. His former students, colleagues and collaborators are invited to submit a manuscript for consideration for publication in this special issue dedicated to his memory.

**Submission:**All authors should follow the author guideline here http://thaijmath.in.cmu.ac.th/index.php/thaijmath/about/submissions#authorGuidelines before submitting their manuscripts and choose "SI: Memory of Professor Charles E. Chidume" when submitting the manuscript.

**Timeline:**

**Special Offer:**

**Invited Guest Editors:**

- Professor Simeon Reich (sreich@technion.ac.il) Technion - Israel Institute of Technology.
- Professor Habtu Zegeye Hailu (habtuzh@yahoo.com) Botswana International University of Science and Technology.
- Professor Eric Uwadiegwu Ofoedu (euofoedu@yahoo.com) Nnamdi Azikiwe University, Awka, Anambra State, Nigeria.
- Professor Bashir Ali (bashiralik@yahoo.com) Bayero University Kano, Nigeria.
- Professor Yekini Shehu (yekini.shehu@unn.edu.ng) Zhejiang Normal University, Jinhua, China.
- Dr. Abubakar Adamu (aadamu@aust.edu.ng) Center of Excellence in Theoretical and Computational Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand.

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### Vol 20, No 2 (2022): June

### Table of Contents

#### Articles

On Lupas-Jain-Beta Operators | |

Prashantkumar Gordhanbhai Patel, Dilek Soylemez, Ovgu Gurel-Yilmaz | 511-525 |

Applications of Multivalued $\mathcal{F}_\delta$-Contraction with Stability Results | |

Gopal Meena, Deepak Singh, Mudasir Younis, Vishal Joshi | 527-544 |

Semi-Analytical Solutions of Batch System Population Balance Models | |

Zehra Pinar | 545-555 |

A Class of Close-to-Convex Functions Satisfying a Differential Inequality | |

Pardeep Kaur, Sukhwinder Singh Billing | 557-562 |

Common Fixed Point Result for $(\alpha,\beta)$-orbital-cyclic Admissible Triplet in Extended $b$-metric Spaces | |

Nehjamang Haokip, Nilakshi Goswami, Binod Chandra Tripathy | 563-576 |

Existence of Solutions of Set-valued Strong Vector Equilibrium Problems | |

Tirth Ram, Parshotam Lal | 577-588 |

Best Proximity Point Results in Generalized Metric Spaces | |

Naeem Saleem, Mujahid Abbas, Sadia Farooq | 589-603 |

Quasi-homeomorphisms between ordered topological spaces | |

Abdelwaheb Mhemdi | 605-610 |

Generalized Ciric's Pairs of Maps and Some Systems of Nonlinear Integral Equations | |

José R Morales, Edixon M Rojas | 611-628 |

On Asymptotically Ideal Invariant Equivalence of Double Sequences | |

Erdinç Dündar, Uğur Ulusu, Fatih Nuray | 629-637 |

Common Fixed Point Theorems for Expansive Type Mappings in Cone Heptagonal Metric Spaces | |

Gizachew Haile, Kidane Koyas, Aynalem Girma | 639-652 |

The Characterization of Fuzzy and Anti Fuzzy Ideals in AG-groupoid | |

Nasreen Kausar, Muhammad Munir, Praveen Agarwal, Kalaichelvan Kalaiarasi | 653-667 |

A Model of Hepatitis C and Blood Pressure via Nano Topological Spaces | |

A.A. NASEF, A.A.El Atik, G.K. REVATHI | 669-677 |

Non-Polynomial Cubic Spline Method for Solving Singularly Perturbed Delay Reaction-Diusion Equations | |

Bekele Badada Tirfesa, Gemechis File Duressa, Habtamu Garoma Debela | 679-692 |

Simple Analytical Formulas for Pricing and Hedging Moment Swaps | |

Kittisak Chumpong, Khamron Mekchay, Sanae Rujivan, Nopporn Thamrongrat | 693-713 |

A Property of $K_{2n+1}$ as the Sum of $n$ Spanning Cycles | |

Hatairat Yingtaweesittikul, Vites Longani | 715-720 |

On the Graded 2-Absorbing Primary Submodules of Graded Multiplication Modules | |

Fatemeh Soheilnia, Shiroyeh Payrovi | 721-728 |

Quaternary Rectangular Bands and Representations of Ternary Semigroups | |

Anak Nongmanee, Sorasak Leeratanavalee | 729-745 |

Finite-Time Stability of a Class of Uncertain Switched Nonlinear Systems with Time-Varying Delay | |

Teerapong La-inchua, Narongsak Yotha | 747-757 |

Soft Theta-Topology Based on Many-Valued Logic | |

Osama Rashed Sayed, Ahmed Mostafa Khalil | 759-783 |

Application of Inverse Possibility Fuzzy Soft Sets over Parameters on Some Semigroups | |

Peerapong Suebsan, Manoj Siripitukdet | 785-795 |

Generalized Cesaro Vector-Valued Sequence Space Using Modulus Function | |

Sudhanshu Kumar, Arvind Kumar Verma | 797-811 |

Stepanov-Like Pseudo Almost Periodic Solutions of Class r in $\alpha$-Norm under the Light of Measure Theory | |

Issa Zabsonre, Abdel Hamid Gamal Nsangou, Moussa El-Khalil Kpoumie, Salifou Mboutngam | 813-841 |

Statistical Convergence in Paranorm Sense on Time Scales | |

Tuba Gulsen, Hikmet Koyunbakan, Emrah Yılmaz, Yavuz Altın | 843-853 |

Some Fixed Point Theorems in K-Metric Type Spaces | |

A. Taheri, Ali Farajzadeh, Suthep Suantai | 855-859 |

df-Statistical Convergence of Order $\alpha$ and df-Strong Cesaro Summability of Order $\alpha$ in Accordance to a Modulus in Metric Spaces | |

Rifat Colak, Emine Kayan | 861-875 |

Cubic Intuitionistic Structure Applied to Commutative Ideals of $BCK$-Algebras | |

Tapan Senapati, Young Bae Jun, Aiyared Iampan, Ronnason Chinram | 877-887 |

Strong Convergence for the Modified Split Monotone Variational Inclusion and Fixed Point Problem | |

Wongvisarut Khuangsatung, Atid Kangtunyakarn | 889-904 |

A Bulk Queueing System with Starting Failure and Repair, Multiple Vacation, Stand-by Server, Closedown and N-Policy | |

S. Karpagam, Govindan Ayyappan | 905-936 |

Representable Autometrized Algebra and MV Algebra | |

B.V. Subba Rao, Akella Kanakam, Phani Yedlapalli | 937-943 |

Fixed Point Theorems of Wardowski Type Mappings in $S_{b}$-Metric Spaces | |

Muhammad Anwar, Dur-e-Shehwar Sagheer, Rashid Ali, Samina B atul | 945-956 |

Dynamics of the Mathematical Model Related to COVID-19 Pandemic with Treatment | |

Özlem Ak Gumus, A. George Maria Selvam, Rajendran Janagaraj | 957-970 |

Convergence of Three-Step Iteration Scheme for Common Fixed Point of Three Berinde Nonexpansive Mappings | |

Seyit Temir | 971-979 |

Intuitionistic Fuzzy F-Normed Space | |

Bivas Dinda, Santanu Kumar Ghosh, Tapas Kumar Samanta | 981-992 |

Best Proximity Coincidence Point Theorem for $G$-Proximal Generalized Geraghty Auxiliary Function in a Metric Space with Graph $G$ | |

Khamsanga Sinsongkham, Watchareepan Atiponrat | 993-1002 |

A Characterization of Maximal Subsemigroups of the Injective Transformation Semigroups with equal Gap and Defect | |

Boorapa Singha | 1003-1010 |

Some New Formulas for Horn's Hypergeometric Functions H_1, H_2, H_3, H_4, H_5, H_6, and H_7 | |

Ayman Shehata, Shimaa I. Moustafa | 1011-1030 |

**The Thai Journal of Mathematics ***is supported by *The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

**Copyright** 2022 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|