STRONG CONVERGENCE THEOREMS FOR A QUASI CONTRACTIVE TYPE MAPPING EMPLOYING A NEW ITERATIVE SCHEME WITH AN APPLICATION

( Surjeet Singh Chauhan ),( Kiran Utreja ),( Mohammad Imdad ),( Md Ahmadullah ) 호남수학회 2017 호남수학학술지 Vol.39 No.1

In this paper, we introduce a new scheme namely: CUIA- iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.

Geraghty type contractions in $b-$metric-like spaces

Surjeet Singh Chauhan(Gonder),Kanika Rana,Mohammad Imdad 강원경기수학회 2022 한국수학논문집 Vol.30 No.4

The main intent of this paper is to prove an existence and uniqueness fixed point result under Geraghty contractions in $b-$metric-like spaces, which remains an extended version of corresponding results in $b-$metric spaces and metric-like spaces. Using two types of Geraghty contractions, an approach is adopted to verify some fixed point results in $b-$metric-like spaces. Our main result is an extension of an earlier result given by Geraghty in $b-$metric-like-space. An example is also provided to demonstrate the validity of our main result. Moreover, as an application of our main result, the existence of solution of a Fredholm integral equation is established which may further be utilized to study the seismic response of dams during earthquakes.

STRONG CONVERGENCE THEOREMS FOR A QUASI CONTRACTIVE TYPE MAPPING EMPLOYING A NEW ITERATIVE SCHEME WITH AN APPLICATION

Chauhan, Surjeet Singh,Utreja, Kiran,Imdad, Mohammad,Ahmadullah, Md The Honam Mathematical Society 2017 호남수학학술지 Vol.39 No.1

In this paper, we introduce a new scheme namely: CUIA-iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.

Coupled fixed point theorems for rational inequality in generalized metric spaces

Deepak Singh,Surjeet Singh Tomar,M.S.Rathore,Varsha Chauhan 영남수학회 2015 East Asian mathematical journal Vol.31 No.1

In modern times, coupled fixed point theorems have been rigorously studied by many researchers in the milieu of partially ordered G- metric spaces using different contractive conditions. In this note, some coupled fixed point theorems using mixed monotone property in partially ordered G-metric spaces are obtained. Furthermore some theorems by omitting the completeness on the space and continuity conditions on function, are obtained. Our results partially generalize some existing results in the present literature. To exemplify our results and to distinguish them from the existing ones, we equip the article with suitable examples.

Efficacy of the parasitoid, Diaeretiella rapae (McIntosh) (Hymenoptera: Braconidae) against Myzus persicae (Sulzer) (Hemiptera: Aphididae) infesting rapeseed-mustard

Soni Saurbh,Kumar Surjeet 한국응용곤충학회 2021 Journal of Asia-Pacific Entomology Vol.24 No.3

Efficacy of Diaeretiella rapae (McIntosh) (Hymenoptera: Braconidae) was determined by studying its biological and behavioural attributes on the aphid, Myzus persicae (Sulzer) (Hemiptera: Aphididae). Total developmental duration of the parasitoid was longer in younger instars compared to that in older instars of aphid. Host age negatively affected the oviposition period and fecundity of the ovipositing parasitoid. Survival of the immatures was higher in older than the younger instars of the aphid. Sex ratio for the parasitoid was female-biased. Longevity of female parasitoid was higher while parasitizing aphid nymphs of younger age groups (1–2 days old) compared to that of older age groups (4–5 days old). Parasitoid showed a higher preference towards second instar of M. persicae both in choice and no-choice tests. Results on mutual interference revealed that per capita searching efficiency decreased from 0.91 to 0.07 as parasitoid densities increased from 1 to 8. Logistic regression exhibited a type II functional response for D. rapae. The estimated values of search-efficiency (a) and handling time (T h ) were 0.038 h − 1 and 1.59 h, respectively. The maximum parasitization rate was 15.08. This investi gation suggests that D. rapae could be an effective candidate for augmentative biological control of M. persicae which infests several plant species of economic importance.

COUPLED FIXED POINT THEOREMS FOR RATIONAL INEQUALITY IN GENERALIZED METRIC SPACES

Singh, Deepak,Tomar, Surjeet Singh,Rathore, M.S.,Chauhan, Varsha The Youngnam Mathematical Society 2015 East Asian mathematical journal Vol.31 No.1

In modern times, coupled fixed point theorems have been rigorously studied by many researchers in the milieu of partially ordered G-metric spaces using different contractive conditions. In this note, some coupled fixed point theorems using mixed monotone property in partially ordered G-metric spaces are obtained. Furthermore some theorems by omitting the completeness on the space and continuity conditions on function, are obtained. Our results partially generalize some existing results in the present literature. To exemplify our results and to distinguish them from the existing ones, we equip the article with suitable examples.

Pharmacological Review of Caralluma R.Br. with Special Reference to Appetite Suppression and Anti-Obesity

Harish Chander Dutt,Surjeet Singh,Bharathi Avula,Ikhlas A. Khan,Yashbir S. Bedi 한국식품영양과학회 2012 Journal of medicinal food Vol.15 No.2

Caralluma fimbriata extract has received Generally Recognized As Safe (GRAS) status for use as a nutraceutical to combat the most serious public health concern (i.e., obesity). More than 260 species grouped under the genus Caralluma (Family Apocynaceae) are distributed in tropical Asia and Mediterranean regions of the globe. Ethnobotanically,some species have been used as traditional and modern dietary ingredients to suppress appetite. Many species of Caralluma are commonly used as traditional medicine for the treatment of rheumatism, diabetes, leprosy, paralysis, and inflammation and have antimalarial, antitrypanosomal, anti-ulcer, antioxidant, antinociceptive, and antiproliferative activities. The genus is known for compounds like pregnane glycosides, flavonoid glycoside, flavones, magastigmane glycosides, pregnane steroids,steroidal glycosides, saturated and unsaturated hydrocarbons, aromatic and nonaromatic volatile compounds, and b-sitosterol. An extract of C. fimbriata (Slimaluna, Gencor Nutrients, Anaheim, CA, USA) is used as an anti-obesity agent and appetite suppressor. It is also seen that the pregnane glycosides isolated and identified from African Hoodia are reported as anti-obesity and appetite-suppressant compounds. On reviewing the studies undertaken on the chemistry, pharmacology, and therapeutic potential of Caralluma, it is concluded that the genus is also composed of pregnane glycosides as one of the major constituents. Availability of pregnane glycosides in Caralluma is an indication of the appetite-suppressant property of this genus. This coupled with the GRAS status of the extract of C. fimbriata has opened the possibility of developing an anti-obesity/appetite-suppressant product from other species of Caralluma. The main objective of this article is to review the studies undertaken on the plant in light of further research for anti-obesity drugs and nutraceuticals from species of Caralluma.

Investigations on magnetic and electrical properties of Zn doped Fe₂O₃ nanoparticles and their correlation with local electronic structures

Kumar, Parmod,Sharma, Vikas,Singh, Jitendra P.,Kumar, Ashish,Chahal, Surjeet,Sachdev, K.,Chae, K.H.,Kumar, Ashok,Asokan, K.,Kanjilal, D. Elsevier 2019 Journal of magnetism and magnetic materials Vol.489 No.-

<P><B>Abstract</B></P> <P>Present work aims at investigating the structural, magnetic and dielectric properties of zinc doped Fe<SUB>2</SUB>O<SUB>3</SUB> nanoparticles (pure, 10%, 20% & 30%) and correlated with their local electronic structures using X-ray absorption near-edge structure (XANES) spectroscopy. X-ray diffraction and Raman measurements infer that doping of Zn cations lead to the formation of secondary phases corresponding to ZnFe<SUB>2</SUB>O<SUB>4</SUB> along with the hematite phase of Fe<SUB>2</SUB>O<SUB>3</SUB>. Magnetic measurements show that magnetization vs magnetic field curve for 10% Zn doping exhibit maximum saturation magnetization (~2.93 × 10<SUP>−3</SUP> emu/g) as well as the coercivity (~956 Oe). The values of these parameters decrease for higher content of Zn. The temperature dependence of dielectric behaviour follows the same trend as that of the lattice parameter and magnetic measurements. The XANES spectra at Fe L- and Fe K-edges indicate partial reduction of Fe<SUP>3+</SUP> ions into Fe<SUP>2+</SUP> upon Zn doping in the Fe<SUB>2</SUB>O<SUB>3</SUB> lattice. However, divalent state is favourable for Zn (i.e. Zn<SUP>2+</SUP>) within the doping range reported in this study.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Zn doped Fe<SUB>2</SUB>O<SUB>3</SUB> nanoparticles. </LI> <LI> Study of magnetic and electrical properties. </LI> <LI> Correlation of magnetic and electrical properties with local electronic structure. </LI> </UL> </P>

Single Crystal Growth and Properties of 2D Antiferromagnet Ni<SUB>1-x</SUB>Zn<SUB>x</SUB>PS₃

Nashra Pistawala,Ankit Kumar,Dibyata Rout,Luminita Harnagea,Surjeet Singh 한국물리학회 2023 새물리 Vol.73 No.12

NiPS₃ is a rare Ni-based negative charge transfer insulator with an antiferromagnetically ordered ground state with Ni spins ordered in a zigzag configuration. Recent reports indicate the presence of strong spin-phonon and spin-charge coupling in NiPS₃. In this study, we report on the growth of high-quality single crystals of Ni<SUB>1-x</SUB>Zn<SUB>x</SUB>PS₃ (x = 0, 0.05, 0.08, 0.13, and 0.14) using the physical vapor transport method. The Raman spectra of all the compositions were measured at 300 K. We show that the phonon mode E<SUP>(2)</SUP><SUB>g</SUB> at 176 cm<SUP>-1</SUP> attributed to the vibration of Ni ions can only be well-fitted using the Breit-Wigner Fano line shape. The parameter |1/q|, which quantifies the strength of the coupling of the phonon E<SUP>(2)</SUP><SUB>g</SUB> to a broad continuum, is found to have a considerably high value of 0.13. The |1/q| parameter increases with increasing Zn doping. Our findings indicate the presence of charge-phonon coupling in NiPS3 at room temperature.