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**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 pages each.

Appear : April, August and December. Occasionally special issues are also published. Papers are published as soon as they are accepted.

**____________________________________________________________________****____________________________________________________________________**

**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]**

**SCImago Journal Rank (SJR) 2017=0.23**

The SJR indicator measures the scientific influence of the average article in a journal, it expresses how central to the global scientific discussion an average article of the journal is. Cites per Doc. (2y) measures the scientific impact of an average article published in the journal, it is computed using the same formula that journal impact factor ™ (

**Thomson Reuters**).**____________________________________________________________________**

**Call for papers**

**A Special Issue of Thai Journal of Mathematics: STRUCTURAL CHANGE MODELING AND OPTIMIZATION IN ECONOMETRICS**

**http://thaijmath.in.cmu.ac.th**

This Special Issue welcomes submissions dealing with the main topic of "structural change/ change point modeling in econometrics" and related issues, including optimization, both theory and applications.

This Special Issue will appear in April, 2019.

Guest Editor: Hung T. Nguyen (hunguyen@nmsu.edu)

Authors should submit their manuscript in PDF file (up to 20 pages),

electronically, DIRECTLY to the Guest Editor at: hunguyen@nmsu.edu

mentioning that it is for this Special Issue.

After the acceptance, authors must send their manuscript in LATEX file

(and the Signed transfer of copyright) to hunguyen@nmsu.edu

CC thaijmath@cmu.ac.th

The authors can find the "Head of LATEX form" from the Journal Website.

This Special Issue will appear in April, 2019.

Guest Editor: Hung T. Nguyen (hunguyen@nmsu.edu)

**Instructions for submission**:Authors should submit their manuscript in PDF file (up to 20 pages),

electronically, DIRECTLY to the Guest Editor at: hunguyen@nmsu.edu

mentioning that it is for this Special Issue.

**Submission deadline**: December 1, 2018After the acceptance, authors must send their manuscript in LATEX file

(and the Signed transfer of copyright) to hunguyen@nmsu.edu

CC thaijmath@cmu.ac.th

The authors can find the "Head of LATEX form" from the Journal Website.

**____________________________________________________________________**

### Vol 16, No 3 (2018): December

### Table of Contents

#### Articles

Generalized $\tau_1\tau_2 $-Closed Sets in Ideal Bitopological Spaces | |

Chalongchai Klanarong, Chawalit Boonpok | 563–575 |

On Strongly Semiprime Modules and Submodules Submodules | |

Hai Q. Dinh, Nguyen Trong Bac, Nico Johannes Groenewald, Dong Thi Hong Ngoc | 577–590 |

On Some Inequalities for Different Kinds of Convexity | |

Merve Avci Ardic, Muhamet Emin Ozdemir | 591–597 |

On Decompositions of Intra-Regular and Left Regular Ordered $\star$-Semigroups | |

Chong-Yih Wu | 599–611 |

New Hadamard's Inequality for $( \alpha _{1}, m_{1})$-$( \alpha _{2}, m_{2})$-Preinvex Functions on the Co-Ordinates | |

khaled boukerrioua, B. Meftah, T. Chiheb | 613–641 |

On the Diophantine Equation $4^x-p^y=3z^2$ where $p$ is a Prime | |

Julius Fergy Tiongson Rabago | 643–650 |

Fine Spectrum of the Generalized Difference Operator $\Delta_{uv}$ on the Sequence Space $c_0$ | |

Parmeshwary Dayal Srivastava, Sudhanshu Kumar | 651–663 |

Global Behavior of a Fourth Order Rational Difference Equation | |

R. Abo-Zeid, M. A. Al-Shabi | 665–674 |

$\epsilon$-Closed Sets | |

Talal Al-Hawary | 675–681 |

Some Inequalities for the $q$-Gamma and the $q$-Polygamma Functions | |

Ahmed Salem | 683–692 |

On Special Weakly Riccisymmetric and Generalized Ricci-Recurrent Trans-Sasakian Structures | |

Sudhakar Kumar Chaubey | 693–707 |

On $\phi-$Quasiconformally Symmetric $N(k)-$Contact Metric Manifolds | |

Avik De, Yoshio Matsuyama | 709–722 |

New Inequalities of Ostrowski Type for Mappings whose Derivatives are $(\alpha, m)$-Convex via Fractional Integrals | |

M. Emin Özdemir, Havva Kavurmaci-Önalan, Merve Avci-Ardic ̧ | 723–731 |

On the Kernel of the Black-Scholes Equation for the Option Price on Future Related to the Black-Scholes Formula | |

Amnuay Kananthai, Somsak Chanaim, Chongkolnee Rungruang | 733–744 |

Multivalued Coincidence Point Results in Partially Ordered Metric Spaces | |

Binayak S. Choudhury, Nikhilesh Metiya | 745–756 |

On Modular Difference Sequence Spaces | |

Parmeshwary Dayal Srivastava, Atanu Manna | 757–774 |

Common Fixed Point Results on Complex Valued $G_b$-Metric Spaces | |

Ozgur Ege1, Ismet Karaca | 775–787 |

On Global Existence of Solutions for Abstract Nonlinear Functional Neutral Integro-Differential Equations with Nonlocal Condition | |

Rupali S. Jain, Machhindra B. Dhakne | 789–799 |

$\Psi$-Stability for Nonlinear Difference Equations | |

T. S. Rao, G. Suresh Kumar, M.S. N. Murty | 801–815 |

Approximating Common Fixed Points for Two $G$-Asymptotically Nonexpansive Mappings with Directed Grahps | |

Manakorn Wattanataweekul | 817–830 |

**Copyright** 2018 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|