Paper's Title:

Fixed Point Results for Integral Type Contractions in R-Metric Space

Author(s):

Samriddhi Ghosh, Ramakant Bhardwaj, Ritu Shrivastava, Vandana Rathore, Satyendra Narayan

Department of Mathematics,
Amity University, Kolkata, West Bengal,
India.
E-mail: ritha98@gmail.com

Department of Mathematics,
Amity University, Kolkata, West Bengal,
India.
E-mail: drrkbhardwaj100@gmail.com

Department of Mathematics,
Bahrain Polytechnic, Isa Town,
Kingdom of Bahrain
E-mail: ritu.shrivastava@polytechnic.bh

Faculty of Science and Technology,
Jagran Lakecity University, Bhopal, Madhya Pradesh,
India.
E-mail: drvandana@jlu.edu.in

School of Computer Science and Technology,
Algoma University, Brampton, Ontario,
Canada.
E-mail: narayan.satyendra@gmail.com

Abstract:

The main aim of the research is to establish some invariant point (fixed point) results under the purview of R-Metric Spaces, for integral type R-contractive mappings. To serve this purpose, concepts of R-continuity, R-convergence and R-preservation has been used. Finally, the obtained results has been used to deduce some invariant point results for Banach, Kannan and Chatterjea type mappings in R-Metric Space. Also some examples and applications have been illustrated to support the findings discussed.

Paper's Title:

Results Concerning Fixed Point for Soft Weakly Contraction In Soft Metric Spaces

Author(s):

Abid Khan, Santosh Kumar Sharma, Anurag Choubey, Girraj Kumar Verma, Umashankar Sharma, Ramakant Bhardwaj

Department of Mathematics,
AUMP, Gwalior,
India.
abid69304@gmail.com

Department of Mathematics,
AUMP, Gwalior,
India.
sksharma1@gwa.amity.edu

Department of Computer Science,
Technocrats Institute of Technology,
Bhopal, MP,
India.
directoracademicstit@gmail.com

Department of Mathematics,
AUMP, Gwalior,
India.
gkverma@gwa.amity.edu

Department of Physics,
RJIT BSF Tekanpur, MP,
India.
ussharma001@gmail.com

School of Applied Science
AUK, WB,
India.
rkbhardwaj100@gmail.com

Abstract:

The basic objective of the proposed research work is to make people acquainted with the concept of soft metric space by generalizing the notions of soft (ψ,φ)-weakly contractive mappings in soft metric space, as well as to look at specific fundamental and topological parts of the underlying spaces. A compatible example is given to explain the idea of said space structure. The theory is very useful in decision making problems and secure transmission as fixed point provides exact output. The fixed-point theorems on subsets of R^m that are useful in game theoretic settings.

Paper's Title:

A Note on Evaluation of a New Class of Integrals Involving Generalized Hypergeometric Function

Author(s):

Madhav Prasad Poudel, Dongkyu Lim^*, Narayan Prasad Pahari, Arjun K. Rathie

School of Engineering,
Pokhara University, Pokhara-30, Kaski,
Nepal.
E-mail: pdmadav@gmail.com

Department of Mathematics Education,
Andong National University, Andong 36729,
Republic of Korea.
E-mail: dklim@anu.ac.kr

Central Department of Mathematics,
Tribhuvan University, Kirtipur, Kathmandu,
Nepal.
E-mail: nppahari@gmail.com

Department of Mathematics,
Vedant College of Engineering & Technology (Rajasthan Technical University), Village: Tulsi,
Jakhamund, Dist. Bundi, Rajasthan State,
India.
E-mail: arjunkumarrathie@gmail.com

Abstract:

In the theory of hypergeometric and generalized hypergeometric series, classical summation theorems such as those of Gauss, Gauss second, Bailey and Kummer for the series ₂F₁; Watson, Dixon, Whipple and Saalshutz play a key role. Applications of the above mentioned summation theorems are well known for the series ₃F₂. In our present investigation, we aim to evaluate twenty five new class of integrals involving generalized hypergeometric function in the form of a single integral of the form:

The results are established with the help of the generalizations of the classical Watson's summation theorem obtained earlier by Lavoie et al.. Fifty interesting integrals in the form of two integrals (twenty five each) have also been given as special cases of our main findings.

Paper's Title:

Using Direct and Fixed Point Technique of Cubic Functional Equation and its Hyers-Ulam Stability

Author(s):

Ramanuja Rao Kotti, Rajnesh Krishnan Mudaliar, Kaushal Neelam Devi, Shailendra Vikash Narayan

Fiji National University,
Department of Mathematics & Statistics,
P.O. Box 5529, Lautoka,
Fiji.
E-mail: ramanuja.kotti@fnu.ac.fj
URL: https://www.fnu.ac.fj

Abstract:

In this present work, we introduce a new type of finite dimensional cubic functional equation of the form

where Φ≥4 is an integer, and derive its general solution. The main purpose of this work is to investigate the Hyers-Ulam stability results for the above mentioned functional equation in Fuzzy Banach spaces by means of direct and fixed point methods.

Paper's Title:

Existence of Optimal Parameters for Damped Sine-Gordon Equation with Variable Diffusion Coefficient and Neumann Boundary Conditions

Author(s):

N. Thapa

Department of Mathematical Sciences,
Cameron University,
2800 West Gore Blvd,
73505 Lawton, Oklahoma,
USA.
E-mail: nthapa@cameron.edu
URL: http://www.cameron.edu/~nthapa/

Abstract:

The parameter identification problem for sine-Gordon equation is of a major interests among mathematicians and scientists.\ In this work we the consider sine-Gordon equation with variable diffusion coefficient and Neumann boundary data. We show the existence and uniqueness of weak solution for sine-Gordon equation. Then we show that the weak solution continuously depends on parameters. Finally we show the existence of optimal set of parameters.

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