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A novel kind of Hermite based Frobenius type Eulerian polynomials
Waseem Ahmad Khan,Kottakkaran Sooppy Nisar,MEHMET ACIKGOZ,UGUR DURAN 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.4
After the inspirational innovation of fuzzy set by Zadeh in 1965, Kramosil and Michalek in 1975 pioneered the concept of fuzziness in metric spaces and very rst they formulated the notion of fuzzy met- ric spaces. Jungck introduced the idea of commutativity (in 1976) and compatibility (1986) in metric spaces and same are utilized by Subrah- manyam (in 1995) in fuzzy metric spaces to prove an analogues version of Jungck result. In this paper, we prove common xed point theorems for a pair of self-maps by introducing a new contraction which neither requires completeness of spaces nor continuity and compatible property of maps. An open problem and an example is given to justify the im- portance of our main result.
Partially degenerate poly-Bernoulli polynomials associated with Hermite polynomials
WASEEM A. KHAN,Moin Ahmad 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.3
In this paper, we derive generating functions for the partially degenerate Hermite poly-Bernoulli polynomials and investigate some properties of these polynomials related to the Stirling numbers of the second kind. Further, we derive the summation formulae and general symmetry identities for that polynomials by using different analytical means on its generating function. Also, generating functions and summation formulae for the polynomials related to partially degenerate Hermite poly- Bernoulli polynomials are obtained as applications of main results.
A Note on $(p,q)$-analogue Type of Frobenius-Genocchi Numbers and Polynomials
Waseem A. Khan,Idrees A. Khan 영남수학회 2020 East Asian mathematical journal Vol.36 No.1
The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and inves- tigate some basic identities and properties for these polynomials and num- bers including addition theorems, difference equations, derivative proper- ties, recurrence relations. We also obtain integral representations, im- plicit and explicit formulas and relations for these polynomials and num- bers. Furthermore, we consider some relationships for Apostol type (p, q)- Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.
Some Properties of the Generalized Apostol Type Hermite-Based Polynomials
KHAN, WASEEM AHMAD Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.3
In this paper, we study some properties of the generalized Apostol type Hermite-based polynomials. which extend some known results. We also deduce some properties of the generalized Apostol-Bernoulli polynomials, the generalized Apostol-Euler polynomials and the generalized Apostol-Genocchi polynomials of high order. Numerous properties of these polynomials and some relationships between $F_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ and $_HF_n{^{({\alpha})}}(x;{\lambda};{\mu};{\nu};c)$ are established. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.
A detector system for searching lost γ-ray source
Khan Waseem,He Chaohui,Cao Yu,Khan Rashid,Yang Weitao 한국원자력학회 2020 Nuclear Engineering and Technology Vol.52 No.7
The aim of this work is to develop a Geiger-Muller (GM) detector system for robot to look for a radioactive source in case of a nuclear emergency or in a high radiation environment. In order to find a radiation source easily, a detector system, including 3 detectors, was designed to search g-ray radiation sources autonomously. First, based on GEANT4 simulation, radiation dose rates in 3 Geiger-Muller (GM) counters were simulated at different source-detector distances, distances between detectors and angles. Various sensitivity analyses were performed experimentally to verify the simulated designed detector system. A mono-energetic 137Cs g-ray source with energy 662 keV and activity of 1.11 GBq was used for the observation. The simulated results were compared with the experimental dose rate values and good agreements were obtained for various cases. Only based on the dose rates in three detectors, the radiation source with a specific source activity and angle was localized in the different location. A method was adopted with the measured dose rates and differences of distances to find the actual location of the lost g-ray source. The corresponding angles of deviation and detection limits were calculated to determine the sensitivity and abilities of our designed detector system. The proposed system can be used to locate radiation sources in low and high radiation environments
ON INTEGRAL OPERATORS INVOLVING THE PRODUCT OF GENERALIZED BESSEL FUNCTION AND JACOBI POLYNOMIAL
WASEEM A. KHAN,M. GHAYASUDDIN,DIVESH SRIVASTAVA 한국전산응용수학회 2018 Journal of applied mathematics & informatics Vol.36 No.5
The aim of this research note is to evaluate two generalized integrals involving the product of generalized Bessel function and Jacobi polynomial by employing the result of Obhettinger [2]. Also, by mean of the main results, we have established an interesting relation in between Kampe de Feriet and Srivastava and Daoust functions. Some interesting special cases of our main results are also indicated.
A STUDY OF POLY-BERNOULLI POLYNOMIALS ASSOCIATED WITH HERMITE POLYNOMIALS WITH q-PARAMETER
Khan, Waseem A.,Srivastava, Divesh The Honam Mathematical Society 2019 호남수학학술지 Vol.41 No.4
This paper is designed to introduce a Hermite-based-poly-Bernoulli numbers and polynomials with q-parameter. By making use of their generating functions, we derive several summation formulae, identities and some properties that is connected with the Stirling numbers of the second kind. Furthermore, we derive symmetric identities for Hermite-based-poly-Bernoulli polynomials with q-parameter by using generating functions.
A NEW CLASS OF PARTIALLY DEGENERATE LAGUERRE-BASED HERMITE-GENOCCHI POLYNOMIALS
Waseem A. Khan,M. GHAYASUDDIN,DIVESH SRIVASTAVA 장전수학회 2022 Advanced Studies in Contemporary Mathematics Vol.32 No.1
In this paper, we introduce partially degenerate Laguerre- based Hermite-Genocchi and investigate their properties and identities. Furthermore, we introduce a generalized form of partially degenerate Laguerre-based Hermite-Genocchi and derive some interesting proper- ties and identities. The results obtained are of general character and can be reduced to yield formulas and identities for relatively simple polyno- mials and numbers.
A note on type 2 degenerate multi-poly-Bernoulli polynomials of the second kind
Waseem A. Khan,M. KAMARUJJAMA 장전수학회 2022 Proceedings of the Jangjeon mathematical society Vol.25 No.1
In this paper, we introduce type 2 degenerate multi-poly- Bernoulli polynomials of the second kind which are defined by using the degenerate multi polyexponential function. We investigate some prop- erties of those numbers and polynomials. Also, we give some identities and relations for the degenerate multi-poly-Bernoulli polynomials and numbers of the second.
CERTAIN NEW EXTENSION OF HURWITZ-LERCH ZETA FUNCTION
WASEEM A. KHAN,M. GHAYASUDDIN,Moin Ahmad 한국전산응용수학회 2019 Journal of applied mathematics & informatics Vol.37 No.1
In the present research paper, we introduce a further exten- sion of Hurwitz-Lerch zeta function by using the generalized extended Beta function dened by Parmar et al. [9]. We investigate its integral represen- tations, Mellin transform, generating functions and dierential formula. In view of diverse applications of the Hurwitz-Lerch Zeta functions, the results presented here may be potentially useful in some related research areas.